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Grothendieck operators on tensor products

Author(s): P. Domanski; M. Lindström; 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.

References:

[A]
F. A. Alexander, Compact and finite rank operators on subspaces of $l^p$, Bull. London Math. Soc. 6 (1974), 341-342. MR 50:8135

[BLV]
J. Bonet, M. Lindström, and M. Valdivia, Two theorems of Josefson-Nissenzweig type for Fréchet spaces, Proc. Amer. Math. Soc. 117 (1993), 363-364. MR 93d:46005

[C]
P. Cembranos, $C(K,E)$ contains a complemented copy of $c_0$, Proc. Amer. Math. Soc. 91 (1984), 556-558. MR 85g:46025

[DL]
P. Domanski and M. Lindström, Grothendieck spaces and duals of injective tensor products, Bull. London Math. Soc. 28 (1996), 617-626. CMP 96:17

[DF]
J. Diestel and B. Faires, Remarks on the classical Banach operator ideals, Proc. Amer. Math. Soc. 58 (1976), 189-196. MR 56:12950

[DFl]
A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland (1993). MR 94e:46130

[DU]
J. Diestel and J. Uhl, Vector measures, AMS Math. Surveys 15 (1977). MR 56:12216

[E]
P. Enflo, A counterexample to the approximation problem in Banach spaces, Acta Math. 130 (1973), 309-317. MR 53:6288

[Fi]
T. Figiel, Factorization of compact operators and applications to the approximation problem, Studia Math. 45 (1973), 191-210. MR 49:1070

[Fr1]
F. J. Freniche, Barrelledness of the spaces of vector-valued and simple functions, Math. Ann. 267 (1984), 479-486. MR 85f:46074

[Fr2]
F. J. Freniche, Grothendieck locally convex spaces of continuous vector-valued functions, Pacific J. Math. 120 (1985), 345-355. MR 87a:46059

[Jh]
K. John, On the compact non-nuclear operator problem, Math. Ann. 287 (1990), 509-514. MR 91f:47029

[Jo]
W. Johnson, Factoring compact operators, Isr. J. Math. 9 (1971), 337-345. MR 44:7318

[K]
N. Kalton, Spaces of compact operators, Math. Ann. 208 (1974), 267-278. MR 49:5904

[Pi]
A. Pietsch, Operator ideals, North-Holland (1980). MR 81j:47001

[R]
F. Räbiger, Beiträge zur Strukturtheorie der Grothendieckräume, Sitzungsber. Heidelb. Akad. Wiss. Math.-Natur. Kl. Abl. 4 (1985). MR 87g:46035

[ST]
E. Saksman and H. O. Tylli, Weak compactness of multiplication operators on spaces of bounded linear operators, Math. Scand. 70 (1992), 91-111. MR 93j:46080

[S]
G. Schlüchtermann, Weak compactness in $L_\infty (\mu ,X)$, J. Funct. Anal. 125 (1994), 379-388. MR 95f:46055

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Additional Information:

P. Domanski
Affiliation: Department of Mathematics, A. Mickiewicz University, 60-769 Poznan, Poland
Email: domanski@math.amu.edu.pl

M. Lindström
Affiliation: Department of Mathematics, Åbo Akademi University, FIN-20500 Åbo, Finland
Email: mikael.lindstrom@abo.fi

G. Schlüchtermann
Affiliation: Mathematisches Institut der Universität München, Theresienstrasse 39, D-80333 München, Germany
Email: schluech@rz.mathematik.uni-muenchen.de

DOI: 10.1090/S0002-9939-97-03763-5
PII: S 0002-9939(97)03763-5
Received by editor(s): August 29, 1995
Received by editor(s) in revised form: January 9, 1996
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society

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