On some Optimization Problems in Not Necessarily Locally Convex Space
On suprema of metrizable vector topologies with trivial dual
On the splitting of twisted sums, and the three space problem for local convexity
On the structure of the dual complexity space: The general case.
On the three-space-problem for topological vector spaces.
On vector spaces and algebras with maximal locally pseudoconvex topologies
Let X be a real or complex vector space. We show that the maximal p-convex topology makes X a complete Hausdorff topological vector space. If X has an uncountable dimension, then different p give different topologies. However, if the dimension of X is at most countable, then all these topologies coincide. This leads to an example of a complete locally pseudoconvex space X that is not locally convex, but all of whose separable subspaces are locally convex. We apply these results to topological algebras,...
Opérations sur les espaces vectoriels topologiques métrisables
p-Envelopes of non-locally convex F-spaces
The p-envelope of an F-space is the p-convex analogue of the Fréchet envelope. We show that if an F-space is locally bounded (i.e., a quasi-Banach space) with separating dual, then the p-envelope coincides with the Banach envelope only if the space is already locally convex. By contrast, we give examples of F-spaces with are not locally bounded nor locally convex for which the p-envelope and the Fréchet envelope are the same.
(p,q)-Convexity in quasi-Banach lattices and applications
Produits tensoriels d'espaces vectoriels topologiques
Pták homomorphism theorem revisited
Rodrigues’ extension (1989) of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting stated that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.
Quasi totally barrelled spaces
Quotient groups of linear topological spaces
Rademacher series and decoupling.
Rademacher series from Orlicz to the present day
We survey some questions on Rademacher series in both Banach and quasi-Banach spaces which have been the subject of extensive research from the time of Orlicz to the present day.
Remarks on independent sequences and dimension in topological linear spaces.
Revisiting Cauty's proof of the Schauder conjecture.
Small operators between Banach and Hilbert spaces
Some fixed point theorems for nonconvex spaces.
Some new classes of topological vector spaces with closed graph theorems
In this note, we investigate non-locally-convex topological vector spaces for which the closed graph theorem holds. In doing so, we introduce new classes of topological vector spaces. Our study includes a direct extension of Pták duality to the non-locally-convex situation.