# Arens regularity of bilinear forms and unital Banach module spaces

Document Type: Research Paper

Author

Faculty member of Mohghegh Ardabili Universsity

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

Main Subjects

### History

• Receive Date: 22 October 2011
• Revise Date: 16 March 2013
• Accept Date: 08 April 2013