A bounded difference property for classes of Banach-valued functions

Author:
Wilbur P. Veith

Journal:
Trans. Amer. Math. Soc. **190** (1974), 49-56

MSC:
Primary 43A60

MathSciNet review:
0387969

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Abstract: Let denote the set of functions *f* from a Hausdorff topological group *G* to a Banach space *E* such that the range of *f* is relatively compact in *E* and is in for each in the dual of *E*, where is a translation-invariant algebra of bounded, continuous, complex-valued functions on *G* with respect to the supremum norm and complex conjugation. has the bounded difference property if whenever is a bounded function such that is in for each *t* in *G*, then *F* is also an element of . A condition on and a condition on *E* are given under which has the bounded difference property. The condition on is satisfied by both the class of almost periodic functions and the class of almost automorphic functions.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1974-0387969-8

Keywords:
Vector-valued almost periodic functions,
vector-valued almost automorphic functions,
bounded difference property,
integration of almost periodic functions,
Banach spaces with no copy of

Article copyright:
© Copyright 1974
American Mathematical Society