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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.

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Weakly compact bilinear forms and Arens regularity
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by A. Ülger PDF
Proc. Amer. Math. Soc. 101 (1987), 697-704 Request permission

Abstract:

Let $X$ and $Y$ be two Banach spaces. We show that a bounded bilinear form $m:X \times Y \to {\mathbf {C}}$ is Arens regular iff it is weakly compact. This result permits us to find very short proofs of some known results as well as some new results. Some of them are: Any ${C^*}$-algebra, the disk algebra and the Hardy class ${H^\infty }$ are Arens regular under every possible product. We also characterize the Arens regularity of certain bilinear mappings.
References
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 101 (1987), 697-704
  • MSC: Primary 46H25; Secondary 46B99, 46G99
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0911036-X
  • MathSciNet review: 911036