(FBa)- and (FBB)-spaces
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.
examples of Fréchet spaces for which Grothendieck's problème des topologies has a positive solution
scientific article; zbMATH DE number 4021942
scientific article