Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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

Author: Kari Ylinen
Journal: Proc. Amer. Math. Soc. 52 (1975), 323-326
MSC: Primary 46L05; Secondary 47B05
MathSciNet review: 0383095
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05, 47B05

Retrieve articles in all journals with MSC: 46L05, 47B05

Additional Information

Keywords: Dual <!– MATH ${C^{\ast }}$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img11.gif" ALT="${C^{\ast }}$">-algebra, weakly completely continuous element, compact element, compact operator
Article copyright: © Copyright 1975 American Mathematical Society