Weakly completely continuous elements of $C^{\ast }$-algebras
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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 ${A^{{\ast }{\ast }}}$.References
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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