Linear Analysis and Representation TheoryA frequently cited scholarly text, this unified treatment constitutes an ideal reference for graduate math students and mathematicians. Its clear, accurate formulations offer a relatively self-contained resource for those studying locally compact groups, Lie groups and algebras, harmonic analysis, and the representation of groups. An introductory chapter on algebras and Banach algebras is followed by a summary of linear functional analysis and examinations of spectral theorem, stable subspaces, and von Neumann algebras. Subsequent chapters explore elementary representation theory in Hilbert space; topological groups, invariant measures, convolutions, and representations; the basic theory of induced representations; and fundamentals of the theory of representations of compact groups. The final chapters offer a concise introduction tothe theory of Lie algebras, Lie groups, and transform groups." |
Contents
HilbertSchmidt Operators | 1 |
The Maximal Ideal Space | 8 |
Commutative Banach Algebras and their Ideals | 16 |
Copyright | |
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A₁ A₂ adjoint arbitrary associated Banach algebra Banach space belongs called choose closed subgroup Co(G commutative compact support contains continuous functions Corollary defined definition denote differentiable direct sum element equivalence class exists finite dimensional follows function f G₁ given Gl(n group G H₁ H₂ Haar measure Hence Hilbert space homomorphism HS operator identity induced representations inner product integral invariant measure invariant subspace irreducible components irreducible representation isometry isomorphism K₁ kernel left ideal left invariant Lemma Let G Lie algebra Lie group linear operator locally compact group Mackey matrix maximal morphism neighborhood Neumann algebra nilpotent non-zero norm obtain open set orthogonal p₁ P₂ projection Proof Proposition 9 prove satisfying Section semisimple Similarly solvable subalgebra subgroup of G subset suppose Theorem tion topological group unimodular unitary representation vector space X₁ zero zonal spherical function