The coproduct of totally convex spaces
The exactness of the projective limit functor on the category of quotients of Frechet spaces
We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L. Waelbroeck [18].
The functor σ²X
We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf Banach spaces.
The projective limit functor for spectra of webbed spaces
We study Palamodov's derived projective limit functor Proj¹ for projective spectra consisting of webbed locally convex spaces introduced by Wilde. This class contains almost all locally convex spaces appearing in analysis. We provide a natural characterization for the vanishing of Proj¹ which generalizes and unifies results of Palamodov and Retakh for spectra of Fréchet and (LB)-spaces. We thus obtain a general tool for solving surjectivity problems in analysis.
The semigroup of Fredholm operators.
The Taylor spectrum and quotient Banach spaces
The universal Banach space with a -suppression unconditional basis
Using the technique of Fraïssé theory, for every constant , we construct a universal object in the class of Banach spaces possessing a normalized -suppression unconditional Schauder basis.
There is no cogenerator of totally convex spaces
Topologies et compactologies