Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles: Basic Representation Theory of Groups and Algebras
J. M.G. Fell, R. S. Doran
Academic Press, Apr 15, 1988 - Mathematics - 746 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 III Locally Compact Groups
Chapter IV Algebraic Representation Theory
Chapter V Locally Convex Representations and Banach Algebras
Chapter VI CAlgebras and Their Representations
Chapter VII The Topology of the Space of Representations
Abelian approximate unit arbitrary assume Banach bundle Banach space Borel measure bounded C*-algebra closure commutative Banach algebra compact Hausdorff space compact subset completely reducible complex Borel measure convergence Corollary countable defined Definition denote dense direct sum element example exists extension finite finite-dimensional follows Gelfand group algebra group G Haar measure Hausdorff space hence Hermitian Hilbert space homomorphism implies integral involution irreducible representation isometry isomorphic Ker(T Lemma Let G linear space linear subspace locally compact group locally compact Hausdorff locally convex representation locally u-measurable Math multiplication neighborhood non-degenerate representation non-void non-zero normed algebra open subset operator set pointwise positive linear functional Prim(A Proof properties Proposition Prove regional topology regular Borel measure regular complex Borel Remark representation of G representation theory respect satisfying sequence spectral measure Suppose Theorem topological group topological space two-sided ideal u-almost unique unitarily equivalent unitary representation vector