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Some Grothendieck's problems in the context of the α-tensor products.

Juan A. López MolinaMaría José Rivera Ortún — 1990

Extracta Mathematicae

The positive and negative results related to the problem of topologies of Grothendieck [2] have given many information on the projective and injective tensor products of Fréchet and DF-spaces. The purpose of this paper is to give some results about analogous questions in αpq-Lapresté's tensor products [4, chapitre 1] and in spaces of dominated operators Pietsch [5] for a class of Fréchet spaces having a certain kind of decomposition studied dy Bonet and Díaz [1] called T-decomposition....

Dunford-Pettis-like properties of projective and natural tensor product spaces.

Jesús M. Fernández CastilloJuan A. López Molina — 1993

Revista Matemática de la Universidad Complutense de Madrid

Several properties of weakly p-summable sequences and of the scale of p-converging operators (i.e., operators transforming weakly p-summable sequences into convergent sequences) in projective and natural tensor products with an lp space are considered. The last section studies the Dunford-Pettis property of order p (i.e., every weakly compact operator is p-convergent) in those spaces.

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