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A generalization of a theorem of A. Grothendieck

✍ Scribed by Oğuz Varol

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
217 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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 → ℒ︁, 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)

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