(FBa)- and (FBB)-spaces
type: Item
instance of: scholarly article
title: (FBa)- and (FBB)-spaces
zbMATH Open document ID: 0628.46068
DOI: 10.1007/BF01184671
author: J. Taskinen
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173931
review text: This paper contains several examples of Fréchet spaces for which Grothendieck's ``problème des topologies'' has a positive solution, i.e. the relevant tensor product has property (BB). Two classes of Fréchet spaces, (FBa)- and (FBB)-spaces, are introduced. If both E and F are (FBa)-spaces regular enough, then it is shown that E\({\hat \otimes}_{\pi}F\) has property (BB). On the other hand, it is shown that e.g. ``most'' Fréchet-Schwartz spaces, certain generalized Köthe- sequence spaces and C(R) are (FBa)-spaces; also Hilbertizable spaces are ``nearly'' (FBa)-spaces. By definition, E is an (FBB)-space if E\({\hat \otimes}_{\pi}F\) has a form of property (BB) for all Fréchet spaces F. It is shown that a Banach space is an (FBB) space if and only if it is an \({\mathcal L}_ 1\)- space. Some generalizations of this result to other Fréchet spaces are also given.
Mathematics Subject Classification ID: 46M05
Mathematics Subject Classification ID: 46A04
zbMATH DE Number: 4021942
zbMATH Keywords: examples of Fréchet spaces for which Grothendieck's problème des topologies has a positive solution
zbMATH Keywords: property (BB)
zbMATH Keywords: (FBB)-spaces
zbMATH Keywords: (FBa)- spaces
zbMATH Keywords: script L1-space
zbMATH Keywords: projective tensor product
zbMATH Keywords: bounded set
MaRDI profile type: Publication
cites work: Q3878195
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OpenAlex ID: W2080928042
description: scientific article; zbMATH DE number 4021942