Quasi-Multipliers on Banach Algebras and Their Topological Properties

This paper presents a comprehensive study of quasi-multipliers on Banach algebras, focusing on their algebraic and topological properties. We define quasi-multipliers as bilinear mappings satisfying specific conditions related to the multiplication structure of the algebra. The existence and uniqueness of quasi-multipliers are studied under the presence of an approximate identity. The extension of quasi-multipliers to the dual space is explored in relation to various topologies such as the bounded convergence topology and y-topology. It is shown that, under suitable assumptions, the space of all quasi-multipliers equipped with a proper topology forms a Banach algebra. Examples from function algebras like L'(G) for locally compact groups are also discussed.

کلیدواژه ها:

Banach algebra ، quasi-multiplier ، left/right multiplier ، approximate identity ، bounded convergence topology ، Y-topology