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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0267403-0
MathSciNet review:
0267403
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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.
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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