A simple condition ensuring the Arens regularity of bilinear mappings

Arikan, Nilgün

doi:10.1090/S0002-9939-1982-0643742-4

A simple condition ensuring the Arens regularity of bilinear mappings
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Proc. Amer. Math. Soc. 84 (1982), 525-531 Request permission

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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