On the derived tensor product functors for (DF)- and Fréchet spaces

Oğuz Varol. "On the derived tensor product functors for (DF)- and Fréchet spaces." Studia Mathematica 180.1 (2007): 41-71. <http://eudml.org/doc/284936>.

@article{OğuzVarol2007,
abstract = {For a (DF)-space E and a tensor norm α we investigate the derivatives $Tor^\{l\}_\{α\}(E,·)$ of the tensor product functor $E ⊗̃_\{α\} ·: → $ from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of $Tor¹_\{α\}(E,F)$, which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.},
author = {Oğuz Varol},
journal = {Studia Mathematica},
keywords = {derived tensor product fuctors; topological tensor products, projective limits; Fréchet spaces; (DF)-spaces},
language = {eng},
number = {1},
pages = {41-71},
title = {On the derived tensor product functors for (DF)- and Fréchet spaces},
url = {http://eudml.org/doc/284936},
volume = {180},
year = {2007},
}

TY - JOUR
AU - Oğuz Varol
TI - On the derived tensor product functors for (DF)- and Fréchet spaces
JO - Studia Mathematica
PY - 2007
VL - 180
IS - 1
SP - 41
EP - 71
AB - For a (DF)-space E and a tensor norm α we investigate the derivatives $Tor^{l}_{α}(E,·)$ of the tensor product functor $E ⊗̃_{α} ·: → $ from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of $Tor¹_{α}(E,F)$, which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.
LA - eng
KW - derived tensor product fuctors; topological tensor products, projective limits; Fréchet spaces; (DF)-spaces
UR - http://eudml.org/doc/284936
ER -