Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles: Banach *-Algebraic Bundles, Induced Representations, and the Generalized Mackey Analysis
J. M.G. Fell, R. S. Doran
Academic Press, May 1, 1988 - Mathematics - 752 pages
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.
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Chapter IX Compact Groups
Chapter X Abelian Groups and Commutative Banach Algebraic Bundles
Chapter XI Induced Representations and the Imprimitivity Theorem
Chapter XII The Generalized Mackey Analysis
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Representations of *-algebras, Locally Compact Groups, and Banach ...
James Michael Gardner Fell,Robert S. Doran
No preview available - 1988
3-positive Abelian group action of G Amer approximate unit Banach algebraic bundle bimodule bundle over G closed subgroup compact Abelian group conjugation construction context correspondence cross-sectional algebra defined definition denote dense direct sum discrete finite groups follows Frobenius Reciprocity group algebra group bundle group G Haar measure hence Hilbert bundle Hilbert space homomorphism implies imprimitivity bimodule Imprimitivity Theorem induced representations inductive limit topology inner product integrated form involution irreducible representations isometric isomorphism Let G Lie groups linear span locally compact group locally convex representation Mackey analysis Mackey obstruction Math non-degenerate representation norm normal subgroup operator inner product orbit positive type Proof Proposition prove regional topology Remark representation of G representation theory satisfying saturated C*-algebraic bundle stability subgroup subgroup of G subspace Suppose system of imprimitivity tensor product topological group unitarily unitary multipliers unitary representation vector verify x e G xe G ye G