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

Oğuz Varol

Oğuz Varol

Studia Mathematica, Tome 178 (2007), p. 41-71 / Harvested from The Polish Digital Mathematics Library

Résumé

For a (DF)-space E and a tensor norm α we investigate the derivatives $T o r_{α}^{l} (E, \cdot)$ of the tensor product functor $E \otimes ̃_{α} \cdot : \to$ from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of $T o r ¹_{α} (E, F)$ , which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.

Publié le : 2007-01-01

Zbl 1138.46045

EUDML-ID : urn:eudml:doc:284936

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     title = {On the derived tensor product functors for (DF)- and Fr\'echet spaces},
     journal = {Studia Mathematica},
     volume = {178},
     year = {2007},
     pages = {41-71},
     zbl = {1138.46045},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-1-4}
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Oğuz Varol. On the derived tensor product functors for (DF)- and Fréchet spaces. Studia Mathematica, Tome 178 (2007) pp. 41-71. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-1-4/