Geodesic
On the derived tensor product functors for (DF)- and Fréchet spaces
Oğuz Varol1
1 Fachbereich C – Mathematik Bergische Universität Wuppertal D-42097 Wuppertal, Germany
Studia Mathematica, Tome 180 (2007) no. 1, pp. 41-71 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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For a (DF)-space $E$ and a tensor norm $\alpha$ we investigate the derivatives $\mathop{\rm Tor}^l_\alpha(E,\cdot)$ of the tensor product functor $E \mathbin{\widetilde{\otimes} _\alpha}{\cdot} :\mathcal{FS}\to \mathcal{LS}$ from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of $\mathop{\rm Tor}^1_\alpha(E,F)$, which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.
DOI : 10.4064/sm180-1-4
Keywords: space tensor norm alpha investigate derivatives mathop tor alpha cdot tensor product functor mathbin widetilde otimes alpha cdot mathcal mathcal category chet spaces category linear spaces necessary sufficient conditions vanishing mathop tor alpha which strongly related exactness tensored sequences presented characterizations nuclear co echelon cases given

Oğuz Varol 1

1 Fachbereich C – Mathematik Bergische Universität Wuppertal D-42097 Wuppertal, Germany 
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Oğuz Varol. On the derived tensor product functors for
 (DF)- and Fréchet spaces. Studia Mathematica, Tome 180 (2007) no. 1, pp. 41-71. doi: 10.4064/sm180-1-4

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