Functional Analysis and Operator Algebras

• Verfasst von: Davidson, Kenneth R. [VerfasserIn]
• Titel: Functional Analysis and Operator Algebras
• Verf.angabe: by Kenneth R. Davidson
• Ausgabe: 1st ed. 2025.
• Verlagsort: Cham
• Verlag: Springer Nature Switzerland
• Jahr: 2025
• Umfang: 1 Online-Ressource(XIV, 797 p. 3 illus., 2 illus. in color.)
• Gesamttitel/Reihe: CMS/CAIMS Books in Mathematics ; 13
• ISBN: 978-3-031-63665-3
• DOI: doi:10.1007/978-3-031-63665-3
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Davidson, Kenneth R., 1951 - : Functional analysis and operator algebras. - Cham : Springer Nature Switzerland, 2025. - xiv, 797 Seiten
• K10plus-PPN: 1922926922
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

Part I Functional Analysis -- 1 Set Theory and Topology -- 2 Banach Spaces -- 3 LCTVSs and Weak Topologies -- 4 Linear Operators -- 5 Compact Operators -- Part II Banach and C*-algebras -- 6 Banach Algebras -- 7 Commutative Banach Algebras -- 8 Noncommutative Banach Algebras -- 9 C*-Algebras -- 10 Von Neumann Algebras -- Part III Operator Theory -- 11 Hardy Spaces -- 12 Isometries and Toeplitz Operators -- 13 Nest Algebras -- 14 Dilation Theory -- 15 Nonselfadjoint Operator Algebras -- 16 Noncommutative Convexity.

Abstract

This book offers a comprehensive introduction to various aspects of functional analysis and operator algebras. In Part I, readers will find the foundational material suitable for a one-semester course on functional analysis and linear operators. Additionally, Part I includes enrichment topics that provide flexibility for instructors. Part II covers the fundamentals of Banach algebras and C*-algebras, followed by more advanced material on C* and von Neumann algebras. This section is suitable for use in graduate courses, with instructors having the option to select specific topics. Part III explores a range of important topics in operator theory and operator algebras. These include USDH^pUSD spaces, isometries and Toeplitz operators, nest algebras, dilation theory, applications to various classes of nonself-adjoint operator algebras, and noncommutative convexity and Choquet theory. This material is suitable for graduate courses and learning seminars, offering instructors flexibility in selecting topics.