Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The trace-class of a full Hilbert algebra


Author: Michael R. W. Kervin
Journal: Trans. Amer. Math. Soc. 178 (1973), 259-270
MSC: Primary 46K15
DOI: https://doi.org/10.1090/S0002-9947-1973-0318900-8
MathSciNet review: 0318900
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The trace-class of a full Hilbert algebra A is the set $\tau (A) = \{ xy|x \in A,y \in A\}$. This set is shown to be a $\ast$-ideal of A, and possesses a norm $\tau$ defined in terms of a positive hermitian linear functional on $\tau (A)$. The norm $\tau$ is in general both incomplete and not an algebra norm, and is also not comparable with the Hilbert space norm $\left \|\right \|$ on $\tau (A)$. However, a one-sided ideal of $\tau (A)$ is closed with respect to one norm if and only if it is closed with respect to the other. The topological dual of $\tau (A)$ with respect to the norm $\tau$ is isometrically isomorphic to the set of left centralizers on A.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46K15

Retrieve articles in all journals with MSC: 46K15


Additional Information

Keywords: Full Hilbert algebra, projection base, left (right) centralizer, trace-class, orthogonal complement
Article copyright: © Copyright 1973 American Mathematical Society