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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
DOI: https://doi.org/10.1090/S0002-9939-1974-0365223-3
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, <!– MATH $\varepsilon$ –> <IMG WIDTH="15" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\varepsilon$">-tensor product, weakly almost periodic, almost periodic, flight vector, reversible vector
Article copyright: © Copyright 1974 American Mathematical Society