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Proceedings of the American Mathematical Society

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

 

 

A note on the compact elements of $ C\sp{\ast} $-algebras


Author: Kari Ylinen
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0296716-3
Article copyright: © Copyright 1972 American Mathematical Society