A. R. Khoddami, H. R. Ebrahimi Vishki
Published 2010-07-09Version 1
Given a Banach space $A$ and fix a non-zero $\varphi\in A^*$ with $\|\varphi\|\leq 1$. Then the product $a\cdot b=\langle\varphi, a\rangle\ b$ turning $A$ into a Banach algebra which will be denoted by $_\varphi A.$ Some of the main properties of $_\varphi A$ such as Arens regularity, $n$-weak amenability and semi-simplicity are investigated.
Arens Regularity of Module Actions and the Second Adjoit of a Derivation
More on the Arens regularity of B(X)
B(l^p) is never amenable
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