Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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.

 

The trace-class of a full Hilbert algebra
HTML articles powered by AMS MathViewer

by Michael R. W. Kervin PDF
Trans. Amer. Math. Soc. 178 (1973), 259-270 Request permission

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
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 46K15
  • Retrieve articles in all journals with MSC: 46K15
Additional Information
  • © Copyright 1973 American Mathematical Society
  • 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