Compact operators and the geometric structure of 𝐶*-algebras

Anoussis, M.; Katsoulis, E.

doi:10.1090/S0002-9939-96-03285-6

Compact operators and the geometric structure of $C^*$-algebras
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by M. Anoussis and E. G. Katsoulis PDF

Proc. Amer. Math. Soc. 124 (1996), 2115-2122 Request permission

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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