The fourth duals of Banach algebras

M. Eshaghi Gordji; S. A. R. Hosseiniun

The fourth duals of Banach algebras

Functional Analysis 2007-05-23 v2

Authors: M. Eshaghi Gordji , S. A. R. Hosseiniun

Abstract

Let $\cal A$ be a Banach algebra. Then $\cal A^{**}$ the second dual of $\cal A$ is a Banach algebra with first (second) Arens product. We study the Arens products of $\cal A^{4}(=({\cal A^{**}})^{**}).$ We found some conditions on $\cal A^{**}$ to be a left ideal in $\cal A^{4}.$ We found the biggest two sided ideal $I$ of ${\cal A},$ in which $I$ is a left (right) ideal of ${\cal A}^{**}$ .

Keywords

banach algebras fourth dual arens product second dual ideals

Cite

@article{arxiv.math/0610207,
  title  = {The fourth duals of Banach algebras},
  author = {M. Eshaghi Gordji and S. A. R. Hosseiniun},
  journal= {arXiv preprint arXiv:math/0610207},
  year   = {2007}
}

Comments

7 pages. To appear in Italian J. of Pure and Appl. Math

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