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

S. Mohammadzadeh; H. R. E. Vishki

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

Functional Analysis 2007-11-13 v1

Authors: S. Mohammadzadeh , H. R. E. Vishki

Abstract

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.

Keywords

Arens regularity bilinear mapping Banach module actions second adjoint derivation dual Banach module

Cite

@article{arxiv.0711.1621,
  title  = {Arens Regularity of Module Actions and the Second Adjoit of a Derivation},
  author = {S. Mohammadzadeh and H. R. E. Vishki},
  journal= {arXiv preprint arXiv:0711.1621},
  year   = {2007}
}