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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A bounded difference property for classes of Banach-valued functions
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by Wilbur P. Veith PDF
Trans. Amer. Math. Soc. 190 (1974), 49-56 Request permission

Abstract:

Let $A(G,E)$ 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 $\phi \circ f$ is in $A(G,C)$ for each $\phi$ in the dual of E, where $A(G,C)$ is a translation-invariant ${C^\ast }$ algebra of bounded, continuous, complex-valued functions on G with respect to the supremum norm and complex conjugation. $A(G,E)$ has the bounded difference property if whenever $F:G \to E$ is a bounded function such that ${\Delta _t}F(x) = F(tx) - F(x)$ is in $A(G,E)$ for each t in G, then F is also an element of $A(G,E)$. A condition on $A(G,C)$ and a condition on E are given under which $A(G,E)$ has the bounded difference property. The condition on $A(G,C)$ is satisfied by both the class of almost periodic functions and the class of almost automorphic functions.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 190 (1974), 49-56
  • MSC: Primary 43A60
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0387969-8
  • MathSciNet review: 0387969