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
K. Haghnejad Azar, "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.
