Linear Analysis and Representation Theory
This frequently cited scholarly reference presents a unified treatment of important subjects from the theory of operators and operator algebras on Hilbert spaces and integration and representation theory for topological groups. The final chapters offer a concise introduction to the theory of Lie algebras, Lie groups, and transform groups. 1973 edition.
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JA Chapter I Algebras and Banach Algebras Algebras and Norms
The Group of Units and the Quasigroup
The Maximal Ideal Space
72 other sections not shown
abelian adjoint arbitrary associated Banach algebra Banach space belongs called choose closed subgroup commutative compact set compact support contains continuous functions continuous linear functional Corollary deﬁned denote differentiable direct sum element equivalence class exists ﬁnd ﬁnite dimensional ﬁrst ﬁxed follows function f given group G Haar measure hand side Hence Hilbert space homomorphism HS operator idempotent implies induced representations inﬁnite inner product integral invariant measure invariant subspace involutive algebra irreducible components irreducible representation isometry isomorphism kernel left ideal left invariant Lemma Let 9 let f Let G Lie algebra Lie group linear manifold linear operator locally compact group matrix minimal MONS morphism Neumann algebra nilpotent non-zero norm obtain open set orthogonal projection Proof regular representation restriction result satisﬁes satisfying Section semisimple sheaf shows Similarly solvable structure subalgebra subgroup of G suppose Theorem tion topological group unimodular unitary representation vector ﬁeld weakly zero zonal spherical function