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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the compact elements of $C^{\ast }$-algebras
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by Kari Ylinen
Proc. Amer. Math. Soc. 35 (1972), 305-306
DOI: https://doi.org/10.1090/S0002-9939-1972-0296716-3

Abstract:

It is shown that for any ${C^ \ast }$-algebra A there is a faithful representation $\pi$ of A on a Hilbert space H such that, for $u \in A$, the map $x \mapsto uxu$ is a compact operator on A if and only if $\pi (u)$ is a compact operator on H.
References
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 305-306
  • MSC: Primary 46L05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0296716-3
  • MathSciNet review: 0296716