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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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The $p$-class in a dual $B^{\ast }$-algebra
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by Pak Ken Wong PDF
Trans. Amer. Math. Soc. 200 (1974), 355-368 Request permission

Abstract:

In this paper, we introduce and study the class ${A_p}(0 < p \leqslant \infty )$ in a dual ${B^ \ast }$-algebra $A$. We show that, for $1 \leqslant p \leqslant \infty ,{A_p}$ is a dual ${A^ \ast }$-algebra which is a dense two-sided ideal of $A$. If $1 < p < \infty$, we obtain that ${A_p}$ is uniformly convex and hence reflexive. We also identify the conjugate space of ${A_p}(1 \leqslant p < \infty )$. This is a generalization of the class ${C_p}$ of compact operators on a Hilbert space.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 200 (1974), 355-368
  • MSC: Primary 46L05; Secondary 46K15
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0358371-X
  • MathSciNet review: 0358371