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

• Autorzy: Oğuz Varol
• Języki publikacji: EN

Abstrakty

EN

For a (DF)-space E and a tensor norm α we investigate the derivatives $Tor^{l}_{α}(E,·)$ of the tensor product functor $E ⊗̃_{α} ·: 𝓕𝓢 → 𝓛𝓢$ 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.

Kategorie tematyczne

• 46A04: Locally convex Fr\'echet spaces and (DF)-spaces
• 46A45: Sequence spaces (including K\"othe sequence spaces)
• 46A32: Spaces of linear operators; topological tensor products; approximation properties
• 46M18: Homological methods (exact sequences, right inverses, lifting, etc.)
• 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 180
• Numer: 1
• Strony: 41-71

Daty

wydano

2007

Twórcy

autor

Oğuz Varol

• Fachbereich C - Mathematik, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany

Identyfikatory

DOI

10.4064/sm180-1-4