Date of Award
2014
Publication Type
Master Thesis
Degree Name
M.Sc.
Department
Mathematics and Statistics
Keywords
Pure sciences, Abstract harmonic analysis, Almost periodic functionals, Banach algebras, Introverted subspaces, Representations, Weakly almost periodic functionals
Supervisor
Monfared, Mehdi S.
Rights
info:eu-repo/semantics/openAccess
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
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.
Recommended Citation
Al-Yassin, Julan, "Representations of banach algebras subordinate to topologically introverted subpaces" (2014). Electronic Theses and Dissertations. 5137.
https://scholar.uwindsor.ca/etd/5137