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On the tensor product of weakly compact operators. (English) Zbl 0778.47016
Continuing the studies of J. Diestel and B. Faires [Proc. Am. Math. Soc. 58, 189-196 (1976; Zbl 0343.47015)] and E. Saksman and H.-O. Tylli [Math. Scand. 70, No. 1, 91-111 (1992; Zbl 0760.47019)], some conditions are given, which ensure the projective and injective tensor product of two weakly compact (w.c. for short) operators to be w.c. For example, the projective tensor roduct of two w.c. operators, one of whose adjoints is absolutely \(p\)-summing, is w.c. And, the inejctive tensor product of two w.c. operators on Pisier spaces is w.c.

MSC:
47A80 Tensor products of linear operators
46B28 Spaces of operators; tensor products; approximation properties
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
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References:
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