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Differential properties of some dense subalgebras of C*-algebras

Published online by Cambridge University Press:  20 January 2009

E. Kissin  and
V. S. Shulman
E. Kissin
Affiliation:
School of Mathematical Sciences, University of North London, Holloway, London N7 8DB, England
V. S. Shulman
Affiliation:
Department of Mathematics, Polytechnic University of Vologda, Vologda, Russia
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Abstract

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The paper studies some classes of dense *-subalgebras B of C*-algebras A whose properties are close to the properties of the algebras of differentiable functions. In terms of a set of norms on B it defines -subalgebras of A and establishes that they are locally normal Q*-subalgebras. If x = x* ∈ B and f(t) is a function on Sp(x), some sufficient conditions are given for f(x) to belong to B. For p = 1, in particular, it is shown that -subalgebras are closed under C∞-calculus. If δ is a closed derivation of A, the algebras D(δp) are -subalgebras of A. In the case when δ is a generator of a one-parameter semigroup of automorphisms of A, it is proved that, in fact, D(δp) are -subalgebras. The paper also characterizes those Banach *-algebras which are isomorphic to subalgebras of C*-algebras.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 3 , October 1994 , pp. 399 - 422
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

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