Date of Award

2014

Degree Type

Thesis

Degree Name

M.Sc.

Department

Mathematics and Statistics

First Advisor

Monfared, Mehdi S.

Keywords

Pure sciences, Abstract harmonic analysis, Almost periodic functionals, Banach algebras, Introverted subspaces, Representations, Weakly almost periodic functionals

Rights

CC BY-NC-ND 4.0

Abstract

We show the existence of a natural bijection between continuous representations of a Banach algebra A on a reflexive Banach space Y subordinate to a topologically introverted subspace X of A * , and normal representations of X * on Y . We define the spaces ap(A) and wap(A) and study some of their properties. We show that if A has a bounded approximate identity, then a functional on A is in wap(A) if and only if it is a coordinate function of a continuous representation of A on a reflexive Banach space. We prove that whenever A has a bounded right approximate identity, then a functional on A is in luc(A) if and only if it is a coordinate function of some norm continuous representation of A on a dual Banach space.

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