Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.




Trace-class and centralizers of an $H^{\ast }$-algebra

Author: Parfeny P. Saworotnow
Journal: Proc. Amer. Math. Soc. 26 (1970), 101-104
MSC: Primary 46.60
MathSciNet review: 0267403
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $A$ be a proper ${H^ \ast }$-algebra. Let $\tau (A) = \{ xy|x,y \in A\}$, let $R(A)$ be the set of all bounded linear operators $S$ on $A$ such that $S(xy) = (Sx)y$ for all $x,y \in A$ and let $C(A)$ be the closed subspace of $R(A)$ generated by the operators of the form $La:x \to ax,a \in A$. It is shown that $\tau (A)$ can be identified with the space of all bounded linear functionals on $C(A)$ and that $R(A)$ is the dual of $\tau (A)$. Also it is proved that $\tau (A)$ is a Banach algebra.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.60

Retrieve articles in all journals with MSC: 46.60

Additional Information

Keywords: Trace-class, <!– MATH ${H^ \ast }$ –> <IMG WIDTH="33" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${H^ \ast }$">-algebra, dual, centralizer, right centralizer, bounded linear functional
Article copyright: © Copyright 1970 American Mathematical Society