φ-Multipliers on Banach Algebras and Topological Modules

Marjan Adib

doi:10.1155/2015/951021

Abstract

We prove some results concerning Arens regularity and amenability of the Banach algebraMφAof allφ-multipliers on a given Banach algebraA. We also considerφ-multipliers in the general topological module setting and investigate some of their properties. We discuss theφ-strict andφ-uniform topologies onMφA. A characterization ofφ-multipliers onL1G-moduleLpG, whereGis a compact group, is given.

Highlights

The concept of a multiplier was introduced by Helgason [1] as follows
Let A be a topological algebra with an approximate identity {eλ : λ ∈ I} and let X be a topological Abimodule
Let A be a topological algebra with an approximate identity {eλ : λ ∈ I} and let (X, τ) be a commutative A-bimodule and φ an idempotent A-module homomorphism on A

Summary

Introduction

The concept of a multiplier was introduced by Helgason [1] as follows. Let A be a commutative and semisimple Banach algebra and let Δ(A) be its maximal ideal space. Let A be a faithful commutative Banach algebra and let φ be an idempotent homomorphism on A. Let A be a faithful commutative Banach algebra and let φ be a homomorphism from A to A with dense range. Let A be a unital Banach algebra and let φ : A → A be a spectrum preserving homomorphism with dense range.

Results

Conclusion