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Grothendieck operators on tensor products

Authors: P. Domanski, M. Lindström and G. Schlüchtermann
Journal: Proc. Amer. Math. Soc. 125 (1997), 2285-2291
MSC (1991): Primary 47A80
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Abstract: We prove that for Banach spaces $E,F,G,H$ and operators $T\in \mathcal {L}(E,G)$, $S\in \mathcal {L}(F,H)$ the tensor product $T\otimes S:E \otimes _\varepsilon F\to G\otimes _\varepsilon H$ is a Grothendieck operator, provided $T$ is a Grothendieck operator and $S$ is compact.

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P. Domanski
Affiliation: Department of Mathematics, A. Mickiewicz University, 60-769 Poznań, Poland

M. Lindström
Affiliation: Department of Mathematics, Åbo Akademi University, FIN-20500 Åbo, Finland

G. Schlüchtermann
Affiliation: Mathematisches Institut der Universität München, Theresienstrasse 39, D-80333 München, Germany

Received by editor(s): August 29, 1995
Received by editor(s) in revised form: January 9, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society