ARENS REGULARITY OF MODULE ACTIONS AND THE SECOND ADJOINT OF A DERIVATION

By S. Mohammadzadeh, H. R. E. Vishki. Bulletin of the Australian Mathematical Society, 2007

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Abstract In this paper, 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 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.

Subfields: Applied Mathematics, Mathematical Physics

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