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Compact operators and the geometric
structure of $C^\ast $-algebras

Authors: M. Anoussis and E. G. Katsoulis
Journal: Proc. Amer. Math. Soc. 124 (1996), 2115-2122
MSC (1991): Primary 47C15, 46B20; Secondary 47D25
MathSciNet review: 1322911
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Abstract: Given a $C^\ast $-algebra $\mathcal {A}$ and an element $A\in \mathcal{A}$, we give necessary and sufficient geometric conditions equivalent to the existence of a representation $(\phi ,\mathcal {H})$ of $\mathcal {A}$ so that $\phi (A)$ is a compact or a finite-rank operator. The implications of these criteria on the geometric structure of $C^\ast $-algebras are also discussed.

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Additional Information

M. Anoussis
Affiliation: Department of Mathematics, University of the Aegean, Karlovasi 83200, Greece

E. G. Katsoulis
Affiliation: Department of Mathematics, East Carolina University, Greenville, North Carolina 27858

Received by editor(s): September 12, 1994
Received by editor(s) in revised form: January 30, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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