Download or read book Topological Algebras with Involution written by M. Fragoulopoulou and published by Elsevier. This book was released on 2005-07-26 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common. Key features: - Lucid presentation- Smooth in reading- Informative- Illustrated by examples- Familiarizes the reader with the non-normed *-world- Encourages the hesitant- Welcomes new comers. - Well written and lucid presentation.- Informative and illustrated by examples.- Familiarizes the reader with the non-normed *-world.
Download or read book Topological Algebras written by and published by Elsevier. This book was released on 2011-10-10 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c). It characterizes the maximal ideals and homomorphisms closed maximal ideals and continuous homomorphisms of topological algebras in general and C(T,F,c) in particular. A considerable inroad is made into the properties of C(T,F,c) as a topological vector space. Many of the results about C(T,F,c) serve to illustrate and motivate results about general topological algebras. Attention is restricted to the algebra C(T,R) of real-valued continuous functions and to the pursuit of the maximal ideals and real-valued homomorphisms of such algebras. The chapter presents the correlation of algebraic properties of C(T,F) with purely topological properties of T. The Stone–Čech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.
Download or read book Topological Algebras and Applications written by Anastasios Mallios and published by American Mathematical Soc.. This book was released on 2007 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fifth International Conference on Topological Algebras and Applications was held in Athens, Greece, from June 27th to July 1st of 2005. The main topic of the Conference was general theory of topological algebras and its various applications, with emphasis on the ``non-normed'' case. in addition to the study of the internal structure of non-normed, and even non-locally convex topological algebras, there are applications to other branches of mathematics, such as differential geometry of smooth manifolds, and mathematical physics, such as quantum relativity and quantum cosmology. Operator theory of unbounded operators and related non-normed topological algebras are intensively studied here. Other topics presented in this volume are topological homological algebra, topological algebraic geometry, sheaf theory and $K$-theory.
Download or read book Topological Algebras written by A. Mallios and published by Elsevier. This book was released on 2011-08-18 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is addressed to those who wish to apply the methods and results of the theory of topological algebras to a variety of disciplines, even though confronted by particular or less general forms. It may also be of interest to those who wish, from an entirely theoretical point of view, to see how far one can go beyond the classical framework of Banach algebras while still retaining substantial results. The need for such an extension of the standard theory of normed algebras has been apparent since the early days of the theory of topological algebras, most notably the locally convex ones. It is worth noticing that the previous demand was due not only to theoretical reasons, but also to potential concrete applications of the new discipline.
Download or read book Topological Algebras and their Applications written by Alexander Katz and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-05-07 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the 8th International Conference of Topological Algebras and Their Applications (ICTAA-2014), held on May 26-30, 2014 in Playa de Villas de Mar Beach, dedicated to the memory of Anastasios Mallios (Athens, Greece). This series of conferences started in 1999 in Tartu, Estonia and were subsequently held in Rabat, Moroco (2000), Oulu, Finland (2001), Oaxaca, Mexico (2002), Bedlewo, Poland (2003), Athens, Greece (2005) and Tartu, Estonia (2008 and 2013). The topics of the conference include all areas of mathematics, connected with (preferably general) topological algebras and their applications, including all kinds of topological-algebraic structures as topological linear spaces, topological rings, topological modules, topological groups and semigroups; bornological-algebraic structures such as bornological linear spaces, bornological algebras, bornological groups, bornological rings and modules; algebraic and topological K-theory; topological module bundles, sheaves and others. Contents Some results on spectral properties of unital algebras and on the algebra of linear operators on a unital algebra Descriptions of all closed maximal one-sided ideals in topological algebras On non self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces Functional calculus on algebras of operators generated by a self-adjoint operator in Pontryagin space Π1 On Gelfand-Naimark type Theorems for unital abelian complex and real locally C*-, and locally JB-algebras Multipliers and strictly real topological algebras Multipliers in some perfect locally m-pseudo-convex algebras Wedderburn structure theorems for two-sided locally m-convex H*-algebras Homologically best modules in classical and quantized functional analysis Operator Grüss inequality Main embedding theorems for symmetric spaces of measurable functions Mapping class groups are linear Subnormable A-convex algebras Commutative BP*-algebras and Gelfand-Naimark’s theorem Discrete nonclosed subsets in maximally nondiscrete topological groups Faithfully representable topological *-algebras: some spectral properties On continuity of complementors in topological algebras Dominated ergodic theorem for isometries of non-commutative Lp-spaces, 1 p p ≠ 2 Ranks and the approximate n-th root property of C*-algebras Dense ideals in topological algebras: some results and open problems
Download or read book Multiplicative Functionals on Topological Algebras written by Taqdir Husain and published by Pitman Advanced Publishing Program. This book was released on 1983 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Book of Involutions written by Max-Albert Knus and published by American Mathematical Soc.. This book was released on 1998 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for graduate students and research mathematicians, this monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. Involutions are viewed as twisted forms of hermitian quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are discussed, as well as: groups of type F4 or G2 arising from exceptional Jordan or composition algebras, the discriminant algebra of an algebra with unitary involution, and the algebra-theoretic counterpart to linear groups of type D4. Annotation copyrighted by Book News, Inc., Portland, OR.
Download or read book The Book of Involutions written by Max-Albert Knus and published by American Mathematical Soc.. This book was released on 1998-06-30 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type $F_4$ or $G_2$ arising from exceptional Jordan or composition algebras. Several results and notions appear here for the first time, notably the discriminant algebra of an algebra with unitary involution and the algebra-theoretic counterpart to linear groups of type $D_4$. This volume also contains a Bibliography and Index. Features: original material not in print elsewhere a comprehensive discussion of algebra-theoretic and group-theoretic aspects extensive notes that give historical perspective and a survey on the literature rational methods that allow possible generalization to more general base rings
Download or read book Topological Geometry written by Ian R. Porteous and published by Cambridge University Press. This book was released on 1981-02-05 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The earlier chapter of this self-contained text provide a route from first principles through standard linear and quadratic algebra to geometric algebra, with Clifford's geometric algebras taking pride of place. In parallel with this is an account, also from first principles, of the elementary theory of topological spaces and of continuous and differentiable maps that leads up to the definitions of smooth manifolds and their tangent spaces and of Lie groups and Lie algebras. The calculus is presented as far as possible in basis free form to emphasize its geometrical flavour and its linear algebra content. In this second edition Dr Porteous has taken the opportunity to add a chapter on triality which extends earlier work on the Spin groups in the chapter on Clifford algebras. The details include a number of important transitive group actions and a description of one of the exceptional Lie groups, the group G2. A number of corrections and improvements have also been made. There are many exercises throughout the book and senior undergraduates in mathematics as well as first-year graduate students will continue to find it stimulating and rewarding.
Download or read book Representations of Algebras Locally Compact Groups and Banach Algebraic Bundles written by J. M.G. Fell and published by Academic Press. This book was released on 1988-05-01 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.
Download or read book Classification of Nuclear C Algebras Entropy in Operator Algebras written by M. Rordam and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. Afactor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.
Download or read book Topological Algebras and Their Applications written by Hugo Arizmendi and published by American Mathematical Soc.. This book was released on 2004 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourth International Conference on Topological Algebras and Their Applications was held in Oaxaca, Mexico. This meeting brought together international specialists and Mexican specialists in topological algebras, locally convex and Banach spaces, spectral theory, and operator theory and related topics. This volume contains talks presented at the conference as well as articles received in response to a call for papers; some are expository and provide new insights, while others contain new research. The book is suitable for graduate students and research mathematicians working in topological vector spaces, topological algebras, and their applications.
Download or read book Generalized Functions written by I. M. Gel'fand and published by Academic Press. This book was released on 2014-05-12 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Functions, Volume 4: Applications of Harmonic Analysis is devoted to two general topics—developments in the theory of linear topological spaces and construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. This volume specifically discusses the bilinear functionals on countably normed spaces, Hilbert-Schmidt operators, and spectral analysis of operators in rigged Hilbert spaces. The general form of positive generalized functions on the space S, continuous positive-definite functions, and conditionally positive generalized functions are also deliberated. This publication likewise considers the mean of a generalized random process, multidimensional generalized random fields, simplest properties of cylinder sets, and definition of Gaussian measures. This book is beneficial to students, specialists, and researchers aiming to acquire knowledge of functional analysis.
Download or read book Generalized Functions Volume 4 written by I. M. Gel′fand and published by American Mathematical Soc.. This book was released on 2016-04-19 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The main goal of Volume 4 is to develop the functional analysis setup for the universe of generalized functions. The main notion introduced in this volume is the notion of rigged Hilbert space (also known as the equipped Hilbert space, or Gelfand triple). Such space is, in fact, a triple of topological vector spaces E⊂H⊂E′, where H is a Hilbert space, E′ is dual to E, and inclusions E⊂H and H⊂E′ are nuclear operators. The book is devoted to various applications of this notion, such as the theory of positive definite generalized functions, the theory of generalized stochastic processes, and the study of measures on linear topological spaces.
Download or read book Calkin Algebras and Algebras of Operators on Banach SPates written by Caradus and published by Routledge. This book was released on 2017-10-19 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the appearance of Banach algebra theory, the interaction between the theories ofBanach algebras with involution and that of bounded linear operators on a Hilbert space hasbeen extensively developed. The connections of Banach algebras with the theory ofbounded linear operators on a Hilbert space have also evolved, and Calkin Algebras andAlgebras of Operators on Banach Spaces provides an introduction to this set of ideas.The book begins with a treatment of the classical Riesz-Schauder theory which takesadvantage of the most recent developments-some of this material appears here for the firsttime. Although the reader should be familiar with the basics of functional analysis, anintroductory chapter on Banach algebras has been included. Other topics dealt with includeFredholm operators, semi-Fredholm operators, Riesz operators. and Calkin algebras.This volume will be of direct interest to both graduate students and research mathematicians.
Download or read book Non Associative Normed Algebras Volume 1 The Vidav Palmer and Gelfand Naimark Theorems written by Miguel Cabrera García and published by Cambridge University Press. This book was released on 2014-07-31 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive bibliography.
Download or read book Classical and Involutive Invariants of Krull Domains written by M.V. Reyes Sánchez and published by Springer. This book was released on 1999-07-31 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to Krull domains and its invariants. The book shows how a serious study of invariants of Krull domains necessitates input from various fields of mathematics, including rings and module theory, commutative algebra, K-theory, cohomology theory, localization theory and algebraic geometry. About half of the book is dedicated to so-called involutive invariants, such as the involutive Brauer group, and is essentially the first to cover these topics. In a structured and methodical way, the work presents a large quantity of results previously scattered throughout the literature. Audience: This volume is recommended as a first introduction to this rapidly developing subject, but will also be useful as a state-of-the-art reference work, both to students at graduate and postgraduate levels and to researchers in commutative rings and algebra, algebraic K-theory, algebraic geometry, and associative rings.
