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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Weakly completely continuous elements of $C^{\ast }$-algebras
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by Kari Ylinen PDF
Proc. Amer. Math. Soc. 52 (1975), 323-326 Request permission

Abstract:

For a $C^{\ast }$-algebra $A$ and $u\epsilon A$, the equivalence of the following three statements is proved: (i) the map $x \mapsto uxu$ is a compact operator on $A$, (ii) (resp. (iii)) the map $x \mapsto ux$ (resp. $x \mapsto xu$) is a weakly compact operator on $A$. The canonical image of a dual ${C^{\ast }}$-algebra $A$ in its bidual ${A^{{\ast }{\ast }}}$ is characterized as the set of the weakly completely continuous elements of ${A^{{\ast }{\ast }}}$.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 323-326
  • MSC: Primary 46L05; Secondary 47B05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0383095-9
  • MathSciNet review: 0383095