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

A simple condition ensuring the Arens regularity of bilinear mappings

Author: Nilgün Arikan
Journal: Proc. Amer. Math. Soc. 84 (1982), 525-531
MSC: Primary 46H05; Secondary 43A15, 46M15
MathSciNet review: 643742
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Abstract: We give a simple criterion for certain Banach algebras to be Arens regular, which applies in particular to the algebras $ {l^1}$ with pointwise multiplication, $ {L^\infty }(G)$, where $ G$ is a compact group with convolution, and the trace-class algebra. This criterion is best established in the more general context of the regularity of bilinear maps, and depends on the existence of extensions of such maps.

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Additional Information

PII: S 0002-9939(1982)0643742-4
Keywords: Arens regularity, bilinear mappings, second duals of Banach algebras
Article copyright: © Copyright 1982 American Mathematical Society