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

Juan A. López Molina; María José Rivera Ortún

Extracta Mathematicae (1990)

- Volume: 5, Issue: 2, page 65-67
- ISSN: 0213-8743

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topLópez Molina, Juan A., and Rivera Ortún, María José. "Some Grothendieck's problems in the context of the αpq-tensor products.." Extracta Mathematicae 5.2 (1990): 65-67. <http://eudml.org/doc/39871>.

@article{LópezMolina1990,

abstract = {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. After that we present the main results in order to give positive answers to the following problems:P1) To localize the bounded sets in Eα ⊗ F.P2) If E and F are DF-spaces, is Eα'pq ⊗ F a DF-space?},

author = {López Molina, Juan A., Rivera Ortún, María José},

journal = {Extracta Mathematicae},

keywords = {Producto tensorial; Espacios localmente convexos; Espacio de Grothendieck; Ideal de operadores},

language = {eng},

number = {2},

pages = {65-67},

title = {Some Grothendieck's problems in the context of the αpq-tensor products.},

url = {http://eudml.org/doc/39871},

volume = {5},

year = {1990},

}

TY - JOUR

AU - López Molina, Juan A.

AU - Rivera Ortún, María José

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

JO - Extracta Mathematicae

PY - 1990

VL - 5

IS - 2

SP - 65

EP - 67

AB - 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. After that we present the main results in order to give positive answers to the following problems:P1) To localize the bounded sets in Eα ⊗ F.P2) If E and F are DF-spaces, is Eα'pq ⊗ F a DF-space?

LA - eng

KW - Producto tensorial; Espacios localmente convexos; Espacio de Grothendieck; Ideal de operadores

UR - http://eudml.org/doc/39871

ER -

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