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

DOI:
https://doi.org/10.1090/S0002-9939-1982-0643742-4

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 with pointwise multiplication, , where 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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DOI:
https://doi.org/10.1090/S0002-9939-1982-0643742-4

Keywords:
Arens regularity,
bilinear mappings,
second duals of Banach algebras

Article copyright:
© Copyright 1982
American Mathematical Society