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?
@article{urn:eudml:doc:39871,
title = {Some Grothendieck's problems in the context of the $\alpha$pq-tensor products.},
journal = {Extracta Mathematicae},
volume = {5},
year = {1990},
pages = {65-67},
zbl = {1230.46059},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39871}
}
López Molina, Juan A.; Rivera Ortún, María José. Some Grothendieck's problems in the context of the αpq-tensor products.. Extracta Mathematicae, Tome 5 (1990) pp. 65-67. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39871/