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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Tensor products and almost periodicity
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by Hugo D. Junghenn PDF
Proc. Amer. Math. Soc. 43 (1974), 99-105 Request permission

Abstract:

Let $E$ and $F$ be locally convex spaces and $G$ their completed $\varepsilon$-tensor product. It is shown that if $S$ and $T$ are weakly almost periodic equicontinuous semigroups of operators on $E$ and $F$ respectively, then, under mild restrictions on $E$ or $F, S \otimes T$ is a weakly almost periodic equicontinuous semigroup of operators on $G$, and the almost periodic and flight vector subspaces of $G$ are related in a natural way to the corresponding subspaces of $E$ and $F$ via the $\varepsilon$-tensor product. Furthermore, if $E$ and $F$ both decompose into a direct sum of these subspaces then so does $G$.
References
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 43 (1974), 99-105
  • MSC: Primary 47D05; Secondary 46M05
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0365223-3
  • MathSciNet review: 0365223