C*-algebras of pure type I_n

Details C*-algebras of pure type I_n C*-algebras of pure type I_n

2012-03-05

arxiv.org/abs/1203.0857v1

Mathematics

Operator Algebras

25 pages

Scientific paper

A C*-algebra is said to be of pure type I_n (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. Intristic characterization (that is, without referring to representations) and models for C*-algebras of pure type I_n are given. Their spectra are introduced and representations of such algebras are investigated. A spectral theorem and a functional calculus for finite systems of elements which generate C*-algebras of pure type I_n are proposed.

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