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Proceedings of the American Mathematical Society

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



Tensor products and almost periodicity

Author: Hugo D. Junghenn
Journal: Proc. Amer. Math. Soc. 43 (1974), 99-105
MSC: Primary 47D05; Secondary 46M05
MathSciNet review: 0365223
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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$.

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Keywords: Semigroup of operators, $ \varepsilon $-tensor product, weakly almost periodic, almost periodic, flight vector, reversible vector
Article copyright: © Copyright 1974 American Mathematical Society