arens regularity of bilinear forms and unital banach module spaces
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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.
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Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 40
issue 2 2014
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