A user's guide to operator algebras
The subject of operator algebras has experienced enormous growth in recent years with significant applications to areas within algebraic mathematics including allied fields as single operator theory, non-self-adjoint operator algebras, K-theory, knot and ergodic theories, and mathematical physics. This book is designed to make these developments accessible to the non-specialist. Proofs are sketched exposing the main concepts and their connections and readers are referred to other sources for complete proofs.
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Spectrum and Order
Examples and Constructions
Von Neumann Algebras
8 other sections not shown
abelian group action of G algebraic tensor product amenable approximate unit automorphism Banach algebra Borel measure C*-dynamical system C*-norm C*-subalgebra CC(G Co(X commutative compact Hausdorff space compact operators completely positive construction continuous field corresponding covariant representation crossed product cyclic decomposition defined denotes direct limit direct sum element exact sequence example extension fact finite type finite-dimensional follows functor Gelfand-Naimark theorem GNS representation group C*-algebra group G groupoid Hausdorff space hence Hilbert space homomorphism homotopy hyperfinite ideal idempotents identity induced injective invariant invertible involution irreducible representations isometry isomorphism L2(G x G Lemma Mn(C morphism multiplication multiplier algebra Neumann algebra nondegenerate nonzero orthogonal pairwise projection proof quotient result self-adjoint semifinite semigroup space H subalgebra subfactor subspace summand surjection tensor product theory topology trace type II factor UHF algebras unique unitary equivalence unitary representation vector bundle weak operator xa G