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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Weakly compact bilinear forms and Arens regularity


Author: A. Ülger
Journal: Proc. Amer. Math. Soc. 101 (1987), 697-704
MSC: Primary 46H25; Secondary 46B99, 46G99
MathSciNet review: 911036
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0911036-X
PII: S 0002-9939(1987)0911036-X
Keywords: Arens regularity, weakly compact bilinear forms, $ {C^*}$-algebra, disk algebra, Hardy class
Article copyright: © Copyright 1987 American Mathematical Society