【摘 要】
：
Following the early pioneering works of Young,Lau,Wong,Duncan,and ülger,almost periodic functionals have been a subject of extensive studies by many author
【机 构】
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UniversityofWindsor,Canada
【出 处】
：
算子代数和调和分析2017年研讨会 (Workshop on Operator Algebras and Harmoni
论文部分内容阅读
Following the early pioneering works of Young,Lau,Wong,Duncan,and ülger,almost periodic functionals have been a subject of extensive studies by many authors.In this talk we discuss some recent results concerning almost periodic functionals and finite-dimensional representations.Perhaps the simplest connection between almost periodic functionals and representation theory is that every coordinate functional of a finite-dimensional representation is almost periodic.In the reverse direction,we show that if A is an involutive Banach algebra,(π;H)is an involutive representation of A,and ζ,η∈H are algebraically cyclic vectors such that πζ,η∈AP(A)(the space of almost periodic functionals on A),then dim H<∞.Next we discuss the properties of a homomorphism αA : A→U(A),where U(A)is a residually finite-dimensional(RFD)Banach algebra.We show that the pair(αA,U(A))satisfies the following properties:(1)the universal property,(2)the existence of a bijection between finite-dimensional representations of A and U(A),(3)the existence of lifts for a large class of AP-functionals on A to AP-functionals on U(A).For these reasons,(αA,U(A))can be regarded as a Banach algebra analogue of the almost periodic compactification of topological groups.We shall also discuss how the adjoint map α*A : U(A)* → A* can be used to construct a Banach algebra(A)(A)(associated with A)and a continuous linear mapping η:(A)(A)→AP(A).When applied to L1(G)(G compact),we find that(A)(L1(G))= A(G)is the Fourier algebra of G,and η(f)= S(f)is the Fourier series expansion of f.The results in this talk are based on a joint work with M.Filali.
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