Sequential convergence in topological vector spaces.
Sequential convergences in a vector lattice
In the present paper we deal with sequential convergences on a vector lattice which are compatible with the structure of .
Sequential retractivities and regularity on inductive limits
In this paper we prove the following result: an inductive limit is regular if and only if for each Mackey null sequence in there exists such that is contained and bounded in . From this we obtain a number of equivalent descriptions of regularity.
Sequentially complete inductive limits and regularity
A notion of an almost regular inductive limits is introduced. Every sequentially complete inductive limit of arbitrary locally convex spaces is almost regular.
Sequentially m-barrelled algebras.
Series de Dirichlet consideradas como espacios de sucesiones.
Set quantities and Tauberian operators.
Sets invariant under projections onto one dimensional subspaces
The Hahn–Banach theorem implies that if is a one dimensional subspace of a t.v.s. , and is a circled convex body in , there is a continuous linear projection onto with . We determine the sets which have the property of being invariant under projections onto lines through subject to a weak boundedness type requirement.
Sets invariant under projections onto two dimensional subspaces
The Blaschke–Kakutani result characterizes inner product spaces , among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace there is a norm 1 linear projection onto . In this paper, we determine which closed neighborhoods of zero in a real locally convex space of dimension at least 3 have the property that for every 2 dimensional subspace there is a continuous linear projection onto with .
Several notions of absolute bases.
Shilov Points and Shilov Boundaries.
Simple construction of spaces without the Hahn-Banach extension property
An elementary construction for an abundance of vector topologies on a fixed infinite dimensional vector space such that has not the Hahn-Banach extension property but the topological dual separates points of from zero is given.
Singular supports. I.
Small ball properties for Fréchet spaces.
We give characterizations of certain properties of continuous linear maps between Fréchet spaces, as well as topological properties on Fréchet spaces, in terms of generalizations of Behrends and Kadets small ball property.
Small deformations of topological algebras
We investigate stability of various classes of topological algebras and individual algebras under small deformations of multiplication.
Small operators between Banach and Hilbert spaces
Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm
Smoothness of a typical convex function
Smulian-Eberlein Spaces
s-numbers of diagonal operators and Besov embeddings