Download or read book Non Commutative Spectral Theory for Affine Function Spaces on Convex Sets written by Erik Magnus Alfsen and published by American Mathematical Soc.. This book was released on 1976 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we develop geometric notions related to self-adjoint projections and one-sided ideals in operator algebras. In the context of affine function spaces on convex sets we define projective units. P-projections, and projective faces which generalize respectively self-adjoint projections p, the maps a [right arrow] pap, and closed faces of state spaces of operator algebras. In terms of these concepts we state a "spectral axiom" requiring the existence of "sufficiently many" projective objects. We then prove the spectral theorem: that elements of the affine function space admit a unique spectral decomposition. This in turn yields a satisfactory functional calculus, which is unique under a natural minimality requirement (that it be "extreme point preserving").
Download or read book Non commutative Spectral Theory for Affine Function Spaces on Convex Sets written by American Mathematical Society and published by . This book was released on 1976 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non commutative Spectral Theory for Affine Function Spaces on Convex Sets written by Aldo Joram Lazar and published by . This book was released on 1976 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non commutative Spectral Theory for Affine Function on Convex Sets written by Erik Magnus Alfsen and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Compact Convex Sets and Boundary Integrals written by Erik M. Alfsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly existed for more than a decade. In fact, the integral representation theorems of Choquet and Bishop -de Leeuw together with the uniqueness theorem of Choquet inaugurated a new epoch in infinite-dimensional convexity. Initially considered curious and tech nically difficult, these theorems attracted many mathematicians, and the proofs were gradually simplified and fitted into a general theory. The results can no longer be considered very "deep" or difficult, but they certainly remain all the more important. Today Choquet Theory provides a unified approach to integral representations in fields as diverse as potential theory, probability, function algebras, operator theory, group representations and ergodic theory. At the same time the new concepts and results have made it possible, and relevant, to ask new questions within the abstract theory itself. Such questions pertain to the interplay between compact convex sets K and their associated spaces A(K) of continuous affine functions; to the duality between faces of K and appropriate ideals of A(K); to dominated extension problems for continuous affine functions on faces; and to direct convex sum decomposition into faces, as well as to integral for mulas generalizing such decompositions. These problems are of geometric interest in their own right, but they are primarily suggested by applica tions, in particular to operator theory and function algebras.
Download or read book Probability Theory and Mathematical Statistics written by Bronius Grigelionis and published by VSP. This book was released on 1990 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Probability Theory and Mathematical Statistics Vol 1 written by B. Grigelionis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "GRIGELIONIS: PROCEEDINGS OF THE FIFTH VILNIUS CONFERE E-BOOK".
Download or read book Convexity Theory and its Applications in Functional Analysis written by L. Asimow and published by Elsevier. This book was released on 2014-06-28 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convexity Theory Appl Functional Analysis
Download or read book Geometry of State Spaces of Operator Algebras written by Erik M. Alfsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we give a complete geometric description of state spaces of operator algebras, Jordan as well as associative. That is, we give axiomatic characterizations of those convex sets that are state spaces of C*-algebras and von Neumann algebras, together with such characterizations for the normed Jordan algebras called JB-algebras and JBW-algebras. These non associative algebras generalize C*-algebras and von Neumann algebras re spectively, and the characterization of their state spaces is not only of interest in itself, but is also an important intermediate step towards the characterization of the state spaces of the associative algebras. This book gives a complete and updated presentation of the character ization theorems of [10]' [11] and [71]. Our previous book State spaces of operator algebras: basic theory, orientations and C*-products, referenced as [AS] in the sequel, gives an account of the necessary prerequisites on C*-algebras and von Neumann algebras, as well as a discussion of the key notion of orientations of state spaces. For the convenience of the reader, we have summarized these prerequisites in an appendix which contains all relevant definitions and results (listed as (AI), (A2), ... ), with reference back to [AS] for proofs, so that this book is self-contained.
Download or read book State Spaces of Operator Algebras written by Erik M. Alfsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of this book is the theory of state spaces of operator algebras and their geometry. The states are of interest because they determine representations of the algebra, and its algebraic structure is in an intriguing and fascinating fashion encoded in the geometry of the state space. From the beginning the theory of operator algebras was motivated by applications to physics, but recently it has found unexpected new applica tions to various fields of pure mathematics, like foliations and knot theory, and (in the Jordan algebra case) also to Banach manifolds and infinite di mensional holomorphy. This makes it a relevant field of study for readers with diverse backgrounds and interests. Therefore this book is not intended solely for specialists in operator algebras, but also for graduate students and mathematicians in other fields who want to learn the subject. We assume that the reader starts out with only the basic knowledge taught in standard graduate courses in real and complex variables, measure theory and functional analysis. We have given complete proofs of basic results on operator algebras, so that no previous knowledge in this field is needed. For discussion of some topics, more advanced prerequisites are needed. Here we have included all necessary definitions and statements of results, but in some cases proofs are referred to standard texts. In those cases we have tried to give references to material that can be read and understood easily in the context of our book.
Download or read book Jordan Algebras in Analysis Operator Theory and Quantum Mechanics written by Harald Upmeier and published by American Mathematical Soc.. This book was released on 1987-01-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Functional Analysis Surveys and Recent Results II written by K.-D. Bierstedt and published by Elsevier. This book was released on 1980-01-01 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Analysis: Surveys and Recent Results II
Download or read book Perfect C ast Algebras written by Charles A. Akemann and published by American Mathematical Soc.. This book was released on 1985 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph investigates [italic]C*-algebras.
Download or read book Probability Theory and Mathematical Statistics written by B. Grigelionis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Probability Theory and Mathematical Statistics".
Download or read book Non Associative Normed Algebras Volume 2 Representation Theory and the Zel manov Approach written by Miguel Cabrera García and published by Cambridge University Press. This book was released on 2018-04-12 with total page 760 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 second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.
Download or read book Mathematical Topics Between Classical and Quantum Mechanics written by Nicholas P. Landsman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.
Download or read book Measure Theory written by A. Bellow and published by Springer. This book was released on 2006-11-14 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt:
