The Schur property on projective and injective tensor products

Botelho, Geraldo; Rueda, Pilar

doi:10.1090/S0002-9939-08-09486-0

The Schur property on projective and injective tensor products
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by Geraldo Botelho and Pilar Rueda PDF

Proc. Amer. Math. Soc. 137 (2009), 219-225 Request permission

Abstract:

The problem of whether the Schur property is passed from a Banach space to its (symmetric) projective $n$-fold tensor product is reformulated in the language of polynomial ideals. As a result, a very closely related question is solved in the negative. It is also proved that the injective tensor product of infrabarrelled locally convex spaces with the Schur property has the Schur property as well.

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