UID:
almahu_9947366500102882
Format:
1 online resource (755 p.)
ISBN:
1-282-25842-7
,
9786612258428
,
0-08-087445-2
Series Statement:
Pure and applied mathematics ; 126
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:
"Banach *-algebraic bundles, induced representations, and the generalized Mackey analysis."
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Front Cover; Banach *-Algebraic Bundles, Induced Representations, and the Generalized Mackey Analysis; Copyright Page; Contents; Introduction to Volume 2 (Chapters VIII to XII); Chapter VIII Banach *-Algebraic Bundles and Their Representations; 1. Multipliers of Algebras; 2. Banach Algebraic Bundles; 3. Banach *-Algebraic Bundles; 4. Semidirect Product Bundles and Central Extension Bundles; 5. The Cross-Sectional Algebra; 6. Partial Cross-Sectional Bundles; 7. Transformation Bundles; 8. Locally Convex Representations of Banach Algebraic Bundles
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9. *-Representations of Banach *-Algebraic Bundles and Unitary Representations of Groups10. Projective Representations of Groups; 11. Integrable Locally Convex Representations; 12. The Recovery of a Fréchet Representation of B from its Integrated Form; 13. The Recovery of a *-Representation of B from its Integrated Form; 14. The Existence of Irreducible *-Representations of Banach *-Algebraic Bundles; 15. The Extension of *-Representations to Multipliers; Application to Semidirect Products and Partial Cross- Sectional Bundles; 16. C*-Algebraic Bundles; the Bundle C*-Completion
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17. Bundle Structures for C*-Algebras the Glimm Algebras; 18. Transformation Bundles and Systems of Imprimitivity; 19. Ergodic Measure Transformation Spaces and Certain Irreducible Systems of Imprimitivity; 20. Functionals of Positive Type on Banach *-Algebraic Bundles; 21. The Regional Topology of *-Representations of Banach *-Algebraic Bundles; 22. Exercises for Chapter VIII; Notes and Remarks; Chapter IX Compact Groups; 1. Preliminary Remarks on Function Spaces; 2. The Peter-Weyl Theorem; 3. Finite-Dimensional Representations of G; 4. Orthogonality Relations
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5. Characters and Central Functions6. The Stone-Weierstrass Theorem for Representations; 7. s-Subspaces and Multiplicity for Locally Convex Representations of G; 8. Weak Féjer Summation; 9. The Structure of the Regular Representation and the Plancherel Formula; 10. Induced Representations and the Frobenius Reciprocity Theorem; 11. The Representations of SU(2); 12. The Representations of SO(3); 13. Exercises for Chapter IX; Notes and Remarks; Chapter X Abelian Groups and Commutative Banach *-Algebraic Bundles; 1. The Character Group; 2. The Theorems of Stone, Bochner and Plancherel
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3. The Fourier Inversion Theorem, Regularity, and Pontryagin Duality4. Commutative Banach *-Algebraic Bundles; 5. Commutative C*-Algebraic Bundles; 6. Exercises for Chapter X; Notes and Remarks; Chapter XI Induced Representations and the Imprimitivity Theorem; 1. Operator Inner Products; 2. Duality for Operator Inner Products; 3. V-bounded Endomorphisms and Modules; Completely Positive Maps; 4. Rigged Modules and Abstractly Induced Representations; 5. General Properties of Abstractly Induced Representations; 6. Imprimitivity Bimodules and the Abstract Imprimitivity Theorem
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7. Topological Versions of the Abstract Imprimitivity Theorem
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English
Additional Edition:
ISBN 0-12-252722-4
Language:
English
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