Arens regularity of bilinear forms and unital Banach module spaces
Author(s):
Abstract:
Assume that $A$, $B$ are Banach algebras and that $m:Atimes Brightarrow B$, $m^prime:Atimes Arightarrow B$ are bounded bilinear mappings. We study the relationships between Arens regularity of $m$, $m^prime$ and the Banach algebras $A$, $B$. For a Banach $A $ -bimodule $B$, we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**} $ -module. Let $Z_{e^{primeprime}}(B^{**})=B^{**}$ where $e^{primeprime}$ is a mixed unit of $A^{**}$. Then $B^*$ factors on both sides with respect to $A$ if and only if $B^{**}$ has a unit as $A^{**} $ -module.
Keywords:
Language:
English
Published:
Bulletin of Iranian Mathematical Society, Volume:40 Issue: 2, 2014
Pages:
505 to 520
https://www.magiran.com/p1284742