The fourth duals of Banach algebras

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

Published 2006-10-05, updated 2007-01-10Version 2

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 ${\cal A}^{**}$.