Date of Award
Mathematics and Statistics
Monfared, Mehdi S.
Pure sciences, Abstract harmonic analysis, Almost periodic functionals, Banach algebras, Introverted subspaces, Representations, Weakly almost periodic functionals
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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.
Al-Yassin, Julan, "Representations of banach algebras subordinate to topologically introverted subpaces" (2014). Electronic Theses and Dissertations. 5137.