Arens Regularity Of Bilinear Forms And Unital Banach Module Spaces

Details Arens Regularity Of Bilinear Forms And Unital Banach Module Spaces Arens Regularity Of Bilinear Forms And Unital Banach Module Spaces

2010-03-17

arxiv.org/abs/1003.3379v1

Mathematics

Functional Analysis

Scientific paper

Assume that $A$, $B$ are Banach algebras and $m:A\times B\to B$, $m^\prime:A\times A\to B$ are bounded bilinear mappings. We will study the relation between Arens regularities of $m$, $m^\prime$ and the Banach algebras $A$, $B$. For Banach $A-bimodule$ $B$, we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is an unital $A^{**}-module$, and we define locally topological center for elements of $A^{**}$ and will show that when locally topological center of mixed unit of $A^{**}$ is $B^{**}$, then $B^*$ factors on both sides with respect to $A$ if and only if $B^{**}$ has a unit as $A^{**}-module$.

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