The higher duals of certain class of Banach algebras

Details The higher duals of certain class of Banach algebras The higher duals of certain class of Banach algebras

2010-07-09

arxiv.org/abs/1007.1651v1

Mathematics

Functional Analysis

6 pages

Scientific paper

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.

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