Characterizations of C* Algebras: the Gelfand Naimark Theorems (Chapman & Hall/CRC Pure and Applied Mathematics)

"The first unified, in-depth discussion of the now classical Gelfand-Naimark theorems, thiscomprehensive text assesses the current status of modern analysis regarding both Banachand C*-algebras. Characterizations of C*-Algebras: The Gelfand-Naimark Theorems focuses on general theoryand basic properties in accordance with readers' needs ... provides complete proofs of theGelfand-Naimark theorems as well as refinements and extensions of the original axioms. . . gives applications of the theorems to topology, harmonic analysis. operator theory.group representations, and other topics ... treats Hermitian and symmetric *-algebras.algebras with and without identity, and algebras with arbitrary (possibly discontinuous)involutions ... includes some 300 end-of-chapter exercises ... offers appendices on functionalanalysis and Banach algebras ... and contains numerous examples and over 400 referencesthat illustrate important concepts and encourage further research. Characterizations of C*-Algebras: The Gelfand-Naimark Theorems is an ideal text for graduatestudents taking such courses as The Theory of Banach Algebras and C*-Algebras: inaddition, it makes an outstanding reference for physicists, research mathematicians in analysis, and applied scientists using C*-algebras in such areas as statistical mechanics, quantumtheory. and physical chemistry."--Provided by publisher. Read more... Abstract: "The first unified, in-depth discussion of the now classical Gelfand-Naimark theorems, thiscomprehensive text assesses the current status of modern analysis regarding both Banachand C*-algebras. Characterizations of C*-Algebras: The Gelfand-Naimark Theorems focuses on general theoryand basic properties in accordance with readers' needs ... provides complete proofs of theGelfand-Naimark theorems as well as refinements and extensions of the original axioms. . . gives applications of the theorems to topology, harmonic analysis. operator theory.group representations, and other topics ... treats Hermitian and symmetric *-algebras.algebras with and without identity, and algebras with arbitrary (possibly discontinuous)involutions ... includes some 300 end-of-chapter exercises ... offers appendices on functionalanalysis and Banach algebras ... and contains numerous examples and over 400 referencesthat illustrate important concepts and encourage further research. Characterizations of C*-Algebras: The Gelfand-Naimark Theorems is an ideal text for graduatestudents taking such courses as The Theory of Banach Algebras and C*-Algebras: inaddition, it makes an outstanding reference for physicists, research mathematicians in analysis, and applied scientists using C*-algebras in such areas as statistical mechanics, quantumtheory. and physical chemistry."--Provided by publisher The Gelfand-naimark Theorems: Historical Perspective -- The Gelfand-naimark Theorem For Commutative C*-algebras -- The Gelfand-naimark Theorem: Arbitrary C*-albebras -- Banach *-albebras: Generalities -- *-representations On A Hilbert Space: A Closer Look -- Hermitian And Symmetric *-algebras -- A Further Weakening Of The C*-axioms -- Geometrical Characterizations Of C*-algebras -- Locally C*-equivalent Algebras -- Applications Of The Characterization Theorems -- Applications Of The Characterization Theorems. Robert S. Doran, Victor A. Belfi. Includes Indexes. Bibliography: P. 373-398. This book gives an account of two celebrated theorems of Gelfand and Naimark for commutative C*-algebras, their tangled history, generalizations and applications, in a form accessible to mathematicians working in various applied fields, and also to students of pure and applied mathematics.