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

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Mohammadzadeh, S.
Vishki, H. R. E.
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Abstract
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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.
Comment: 15 pages. To appear in Bull. Austral. Math. Soc
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Mathematics - Functional Analysis, 46H20, 46H25
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