Download or read book Operator Theory Functional Analysis and Applications written by M. Amélia Bastos and published by Springer Nature. This book was released on 2021-03-31 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.
Download or read book Dilation Theory Toeplitz Operators and Other Topics written by Constantin Apostol and published by . This book was released on 1983 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Glimpse at Hilbert Space Operators written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2011-04-13 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Richard Halmos, who lived a life of unbounded devotion to mathematics and to the mathematical community, died at the age of 90 on October 2, 2006. This volume is a memorial to Paul by operator theorists he inspired. Paul’sinitial research,beginning with his 1938Ph.D. thesis at the University of Illinois under Joseph Doob, was in probability, ergodic theory, and measure theory. A shift occurred in the 1950s when Paul’s interest in foundations led him to invent a subject he termed algebraic logic, resulting in a succession of papers on that subject appearing between 1954 and 1961, and the book Algebraic Logic, published in 1962. Paul’s ?rst two papers in pure operator theory appeared in 1950. After 1960 Paul’s research focused on Hilbert space operators, a subject he viewed as enc- passing ?nite-dimensional linear algebra. Beyond his research, Paul contributed to mathematics and to its community in manifold ways: as a renowned expositor, as an innovative teacher, as a tireless editor, and through unstinting service to the American Mathematical Society and to the Mathematical Association of America. Much of Paul’s in?uence ?owed at a personal level. Paul had a genuine, uncalculating interest in people; he developed an enormous number of friendships over the years, both with mathematicians and with nonmathematicians. Many of his mathematical friends, including the editors ofthisvolume,whileabsorbingabundantquantitiesofmathematicsatPaul’sknee, learned from his advice and his example what it means to be a mathematician.
Download or read book Classical Function Theory Operator Dilation Theory and Machine Computation on Multiply Connected Domains written by Jim Agler and published by American Mathematical Soc.. This book was released on 2008 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work begins with the presentation of generalizations of the classical Herglotz Representation Theorem for holomorphic functions with positive real part on the unit disc to functions with positive real part defined on multiply-connected domains. The generalized Herglotz kernels that appear in these representation theorems are then exploited to evolve new conditions for spectral set and rational dilation conditions over multiply-connected domains. These conditions form the basis for the theoretical development of a computational procedure for probing a well-known unsolved problem in operator theory, the so called rational dilation conjecture. Arbitrary precision algorithms for computing the Herglotz kernels on circled domains are presented and analyzed. These algorithms permit an effective implementation of the computational procedure which results in a machine generated counterexample to the rational dilation conjecture.
Download or read book Dilation Theory Toeplitz Operators and Other Topics written by Apostol and published by Birkhäuser. This book was released on 1983 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Course in Operator Theory written by John B. Conway and published by American Mathematical Soc.. This book was released on 2000 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation theory, mathematical physics, and more. This text covers the central themes of operator theory, presented with the excellent clarity and style that readers have come to associate with Conway's writing. Early chapters introduce and review material on $C^*$-algebras, normal operators, compact operators, and non-normal operators. Some of the major topics covered are the spectral theorem, the functional calculus, and the Fredholm index. In addition, some deep connections between operator theory and analytic functions are presented. Later chapters cover more advanced topics, such as representations of $C^*$-algebras, compact perturbations, and von Neumann algebras. Major results, such as the Sz.-Nagy Dilation Theorem, the Weyl-von Neumann-Berg Theorem, and the classification of von Neumann algebras, are covered, as is a treatment of Fredholm theory. The last chapter gives an introduction to reflexive subspaces, which along with hyperreflexive spaces, are one of the more successful episodes in the modern study of asymmetric algebras. Professor Conway's authoritative treatment makes this a compelling and rigorous course text, suitable for graduate students who have had a standard course in functional analysis.
Download or read book The Extended Field of Operator Theory written by Michael A. Dritschel and published by Springer Science & Business Media. This book was released on 2007-06-25 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions originating from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Newcastle upon Tyne in July 2004. The articles expertly cover a broad range of material at the cutting edge of functional analysis and its applications. The works are written by world authorities in their specialities.
Download or read book Introduction to Operator Space Theory written by Gilles Pisier and published by Cambridge University Press. This book was released on 2003-08-25 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of operator spaces, emphasising applications to C*-algebras.
Download or read book Completely Bounded Maps and Operator Algebras written by Vern Paulsen and published by Cambridge University Press. This book was released on 2002 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Download or read book Multivariable Operator Theory written by Ernst Albrecht and published by Springer Nature. This book was released on 2024-01-22 with total page 893 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Download or read book An Indefinite Excursion in Operator Theory written by Aurelian Gheondea and published by Cambridge University Press. This book was released on 2022-07-28 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a modern, readable introduction to spaces with indefinite inner product and their operator theory.
Download or read book Harmonic Analysis of Operators on Hilbert Space written by Béla Sz Nagy and published by Springer Science & Business Media. This book was released on 2010-09-01 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Download or read book Operator Theory and Arithmetic in H infinity written by Hari Bercovici and published by American Mathematical Soc.. This book was released on 1988 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jordan's classification theorem for linear transformations on a finite-dimensional vector space is a natural highlight of the deep relationship between linear algebra and the arithmetical properties of polynomial rings. Because the methods and results of finite-dimensional linear algebra seldom extend to or have analogs in infinite-dimensional operator theory, it is therefore remarkable to have a class of operators which has a classification theorem analogous to Jordan's classical result and has properties closely related to the arithmetic of the ring $H^{\infty}$ of bounded analytic functions in the unit disk. $C_0$ is such a class and is the central object of study in this book.A contraction operator belongs to $C_0$ if and only if the associated functional calculus on $H^{\infty}$ has a nontrivial kernel. $C_0$ was discovered by Bela Sz.-Nagy and Ciprian Foias in their work on canonical models for contraction operators on Hilbert space. Besides their intrinsic interest and direct applications, operators of class $C_0$ are very helpful in constructing examples and counterexamples in other branches of operator theory. In addition, $C_0$ arises in certain problems of control and realization theory.In this survey work, the author provides a unified and concise presentation of a subject that was covered in many articles. The book describes the classification theory of $C_0$ and relates this class to other subjects such as general dilation theory, stochastic realization, representations of convolution algebras, and Fredholm theory. This book should be of interest to operator theorists as well as theoretical engineers interested in the applications of operator theory. In an effort to make the book as self-contained as possible, the author gives an introduction to the theory of dilations and functional models for contraction operators. Prerequisites for this book are a course in functional analysis and an acquaintance with the theory of Hardy spaces in the unit disk. In addition, knowledge of the trace class of operators is necessary in the chapter on weak contractions.
Download or read book Operator Theory Operator Algebras and Their Interactions with Geometry and Topology written by Raul E Curto and published by Springer Nature. This book was released on 2020-12-12 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.
Download or read book Operator Theory and Arithmetic in H Infinity written by Hari Bercovici and published by . This book was released on 2014-05-22 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to the theory of dilations and functional models for contraction operators. This book describes the classification theory of $C_0$ and relates this class to other subjects such as general dilation theory, stochastic realization, and Fredholm theory. It is suitable for operator theorists.
Download or read book Operator Valued Measures Dilations and the Theory of Frames written by Deguang Han and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop elements of a general dilation theory for operator-valued measures. Hilbert space operator-valued measures are closely related to bounded linear maps on abelian von Neumann algebras, and some of their results include new dilation results for bounded linear maps that are not necessarily completely bounded, and from domain algebras that are not necessarily abelian. In the non-cb case the dilation space often needs to be a Banach space. They give applications to both the discrete and the continuous frame theory. There are natural associations between the theory of frames (including continuous frames and framings), the theory of operator-valued measures on sigma-algebras of sets, and the theory of continuous linear maps between -algebras. In this connection frame theory itself is identified with the special case in which the domain algebra for the maps is an abelian von Neumann algebra and the map is normal (i.e. ultraweakly, or weakly, or w*) continuous.
Download or read book Introduction to Operator Theory and Invariant Subspaces written by B. Beauzamy and published by Elsevier. This book was released on 1988-10-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph only requires of the reader a basic knowledge of classical analysis: measure theory, analytic functions, Hilbert spaces, functional analysis. The book is self-contained, except for a few technical tools, for which precise references are given. Part I starts with finite-dimensional spaces and general spectral theory. But very soon (Chapter III), new material is presented, leading to new directions for research. Open questions are mentioned here. Part II concerns compactness and its applications, not only spectral theory for compact operators (Invariant Subspaces and Lomonossov's Theorem) but also duality between the space of nuclear operators and the space of all operators on a Hilbert space, a result which is seldom presented. Part III contains Algebra Techniques: Gelfand's Theory, and application to Normal Operators. Here again, directions for research are indicated. Part IV deals with analytic functions, and contains a few new developments. A simplified, operator-oriented, version is presented. Part V presents dilations and extensions: Nagy-Foias dilation theory, and the author's work about C1-contractions. Part VI deals with the Invariant Subspace Problem, with positive results and counter-examples. In general, much new material is presented. On the Invariant Subspace Problem, the level of research is reached, both in the positive and negative directions.
