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

López 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 -