C*-Algebras and Applications
The theory of C*-algebras dates from the discovery by Gelfand and Naimark that uniformly closed self-adjoint operator algebras on Hilbert space—unlike the rings studied by von Neumann and Murray—could be characterized in simple intrinsic algebraic terms, independently of their action on Hilbert space. This opened up the study of the algebraic isomorphism classes of such algebras, in the sense of emphasizing its cogency. It was soon found that C*-algebras have certain applications in quantum mechanics, and especially in quantum field theory, in parts of group representation theory, and some other areas, in which W*-algebras could not be substituted.
KeywordsHilbert Space Irreducible Representation Pure State Compact Hausdorff Space Approximate Identity
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