Arens Regularity of Module Actions and the Second Adjoit of a Derivation

Details Arens Regularity of Module Actions and the Second Adjoit of a Derivation Arens Regularity of Module Actions and the Second Adjoit of a Derivation

2007-11-10

arxiv.org/abs/0711.1621v1

Mathematics

Functional Analysis

15 pages. To appear in Bull. Austral. Math. Soc

Scientific paper

In this paper, first we give a simple criterion for the Arens regularity of a bilinear mapping on normed spaces, which applies in particular to Banach module actions and then we investigate those conditions under which the second adjoint of a derivation into a dual Banach module is again a derivation. As a consequence of the main result, a simple and direct proof for several older results is also included.

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