Premium
A generalization of a theorem of A. Grothendieck
Author(s) -
Varol Oğuz
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410484
Subject(s) - mathematics , injective function , tensor product , pure mathematics , tensor product of modules , functor , tensor product of hilbert spaces , tensor product of algebras , type (biology) , product (mathematics) , generalization , space (punctuation) , fundamental theorem , fixed point theorem , tensor contraction , mathematical analysis , geometry , ecology , linguistics , philosophy , biology
In this article we characterize the quasi‐barrelledness of the projective tensor product of a coechelon space of type one k 1 ( A ) with a Fréchet space, including homological conditions as exactness properties of the corresponding tensor product functor k 1 ( A ) ·: ℱ → ℒ, acting from the category of Fréchet spaces to the category of linear spaces, resp. the vanishing of its first right derivative Tor 1 π ( k 1 ( A ),.). This generalizes and extends a classical theorem of A. Grothendieck ([13, Chap. II, §4, No. 3, Theorem 15]). Further we present an analogous theorem for complete coechelon spaces of type zero and the injective tensor product and results concerning the stronger property of barrelledness. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)