On the derived tensor product functors for (DF)- and Fréchet spaces
Volume 180 / 2007
Studia Mathematica 180 (2007), 41-71
MSC: Primary 46M18, 46A32; Secondary 46A04, 46A11, 46A45.
DOI: 10.4064/sm180-1-4
Abstract
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.
