UID:
almahu_9947366496402882
Format:
1 online resource (771 p.)
ISBN:
1-282-25843-5
,
9786612258435
,
0-08-087444-4
Series Statement:
Pure and applied mathematics ; v. 125
Content:
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.
Note:
Description based upon print version of record.
,
Front Cover; Basic Representation Theory of Groups and Algebras; Copyright Page; Contents; Preface; Introduction to Volume 1 (Capter I to VII); Chapter I Preliminaries; 1. Logical, Set and Functional Notation; 2. Numerical Notation; 3. Topology; 4. Algebra; 5. Seminorms, Normed Spaces, Normed Algebras; 6. Hilbert Spaces; 7. Exercises for Chapter I; Notes and Remarks; Chapter II Integration Theory and Banach Bundles; 1. δ-Rings, Measures, and Measurable Functions; 2. Integration of Complex Functions; 3. The Outsize Lp Spaces; 4. Local Measurability Structures
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5. Integration of Functions with Values in a Banach Space6. Integration of Functions with Values in a Locally Convex Space; 7. The Radon-Nikodym Theorem and Related Topics; 8. Measures on Locally Compact Hausdorff Spaces; 9. Product Measures and Fubini's Theorem; 10. Measure Transformations; 11. Projection-Valued Measures and Spectral Integrals; 12. The Analogue of the Riesz Theorem for Projection-Valued Measures; 13. Banach Bundles; 14. Banach Bundles over Locally Compact Base Spaces'; 15. Integration in Banach Bundles over Locally Compact Spaces; 16. Fubini Theorems for Banach Bundles
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17. Exercises for Chapter IINotes and Remarks; Chapter III Locally Compact Groups; 1. Topological Groups and Subgroups; 2. Quotient Spaces and Homomorphisms; 3. Topological Transformation Spaces; 4. Direct and Semidirect Products; 5. Group Extensions; 6. Topological Fields; 7. Haar Measure; 8. The Modular Function; 9. Examples of Haar Measure and the Modular Function; 10. Convolution and Involution of Measures on G; 11. Convolution of functions, the L1, group algebra; 12. Relations between Measure and Topology on G; 13. Invariant Measures on Coset Spaces
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14. Quasi-Invariant Measures on Coset Spaces15. Exercises for Chapter III; Notes and Remarks; Chapter IV Algebraic Representation Theory; 1. Fundamental Definitions; 2. Complete Reducibility and Multiplicity for Operator Sets; 3. Representations of Groups and Algebras; 4. The Extended Jacobson Density Theorem; 5. Finite-dimensional Semisimple Algebras; 6. Application to Finite Groups; 7. The Complex Field and *-Algebras; 8. Exercises for Chapter IV; Notes and Remarks; Chapter V Locally Convex Representations and Banach Algebras; 1. Locally Convex Representations; Fundamental Definitions
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2. Extending Locally Convex Representations of Two-sided Ideals3. The Naimark Relation; 4. Elementary Remarks on Normed Algebras; Examples; 5. The Spectrum; 6. Spectra in Banach Algebras, Mazur's Theorem, Gelfand's Theorem; 7. Commutative Banach Algebras; 8. Function Algebras and Co(S); 9. Factorization in Banach Algebras; 10. Exercises for Chapter V; Notes and Remarks; Chapter VI C*-Algebras and Their *-Representations; 1. *-Algebras; Elementary Remarks and Examples; 2. Symmetric *-Algebra; 3. C*-Algebras; 4. Commutative C*-Algebras; 5. Spectra in Subalgebras of C*-Algebras
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6. The Functional Calculus in C*-Algebras
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English
Additional Edition:
ISBN 0-12-252721-6
Language:
English
