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.
Haghnejad Azar, K. (2014). Arens regularity of bilinear forms and unital Banach module spaces. Bulletin of the Iranian Mathematical Society, 40(2), 505–520.
MLA
Haghnejad Azar, K. "Arens regularity of bilinear forms and unital Banach module spaces", Bulletin of the Iranian Mathematical Society, 40, 2, 2014, 505–520.
HARVARD
Haghnejad Azar, K. (2014). 'Arens regularity of bilinear forms and unital Banach module spaces', Bulletin of the Iranian Mathematical Society, 40(2), pp. 505–520.
CHICAGO
Haghnejad Azar, K., "Arens regularity of bilinear forms and unital Banach module spaces." Bulletin of the Iranian Mathematical Society, 40 2 (2014): 505–520,
VANCOUVER
Haghnejad Azar K. Arens regularity of bilinear forms and unital Banach module spaces. BIMS. 2014;40(2):505–520.
