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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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Weakly almost periodic functions and almost convergent functions on a group
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by Ching Chou PDF
Trans. Amer. Math. Soc. 206 (1975), 175-200 Request permission

Abstract:

Let $G$ be a locally compact group, $UC(G)$ the space of bounded uniformly continuous complex functions on $G,{C_0}(G)$ the subspace of $UC(G)$ consisting of functions vanishing at infinity. Let $W(G)$ be the space of weakly almost periodic functions on $G$ and ${W_0}(G)$ the space of functions in $W(G)$ such that their absolute values have zero invariant mean. If $G$ is amenable let $F(G)$ be the space of almost convergent functions in $UC(G)$ and ${F_0}(G)$ the space of functions in $F(G)$ such that their absolute values are almost convergent to zero. The inclusive relations among the above-mentioned spaces are studied. It is shown that if $G$ is noncompact and satisfies certain conditions, e.g. $G$ is nilpotent, then each of the quotient Banach spaces $UC(G)/W(G),{W_0}(G)/{C_0}(G),{F_0}(G)/{W_0}(G)$ contains a linear isometric copy of ${l^\infty }$. On the other hand, an example of a noncompact group $G$ is given which satisfies the condition that ${C_0}(G) = {W_0}(G)$.
References
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 206 (1975), 175-200
  • MSC: Primary 43A60; Secondary 43A07
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0394062-8
  • MathSciNet review: 0394062