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Excising States of C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Charles A. Akemann ,
Joel Anderson  and
Gert K. Pedersen
Charles A. Akemann
Affiliation:
University of California at Santa Barbara, Santa Barbara, California
Joel Anderson
Affiliation:
Pennsylvania State University, University Park, Pennsylvania
Gert K. Pedersen
Affiliation:
Universitetsparken 5, Copenhagen, Denmark
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A net {aα} of positive, norm one elements of a C*-algebra A excises a state f of A if

This notion has been used explicitly by the second author [4, 5, 6] for pure states, but the present paper will explore it more fully. The name is motivated by the following example. Let K be the unit disk in the complex plane, A = C(K) and f(a) = a(0). Define an(reiθ) = ϕn(r), where

Note that the sets {t ∊ K:an(t) ∊ 0} form rings about 0 with radii tending to 0. In this sense the sequence {an} “cuts out” the state f and, in the limit, isolates it from all other states.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 5 , 01 October 1986 , pp. 1239 - 1260
Copyright
Copyright © Canadian Mathematical Society 1986

References

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