On the complex of Sobolev spaces associated with an abstract Hilbert complex.
On the complexity of Hamel bases of infinite-dimensional Banach spaces
We call a subset S of a topological vector space V linearly Borel if for every finite number n, the set of all linear combinations of S of length n is a Borel subset of V. It is shown that a Hamel basis of an infinite-dimensional Banach space can never be linearly Borel. This answers a question of Anatoliĭ Plichko.
On the complexity of some classes of Banach spaces and non-universality
These notes are dedicated to the study of the complexity of several classes of separable Banach spaces. We compute the complexity of the Banach-Saks property, the alternating Banach-Saks property, the complete continuous property, and the LUST property. We also show that the weak Banach-Saks property, the Schur property, the Dunford-Pettis property, the analytic Radon-Nikodym property, the set of Banach spaces whose set of unconditionally converging operators is complemented in its bounded operators,...
On the composition of distributions and .
On the Composition Operator in AC[a,b].
Denote by F the composition operator generated by a given function f: R --> R, acting on the space of absolutely continuous functions. In this paper we prove that the composition operator F maps the space AC[a,b] into itself if and only if f satisfies a local Lipschitz condition on R.
On the Conjugate Endomorphism in the Infinite Index Case.
On the conjugates of some function spaces
On the connectedness of the set of fixed points of a compact operator in the Fréchet space
On the connection between the real and the complex interpolation method for several Banach spaces
On the constants for some Sobolev imbeddings.
On the constants of basic sequences in Banach spaces
On the Construction of Iteration Methods for Linear Equations in Banach Spaces by Summation Methods. (Short Communication).
On the Construction of Iteration Methods for Linear Equations in Banach Spaces by Summation Methods.
On the continuity and differentiability properties of convex functionals
On the continuity of Bessel potentials in Orlicz spaces.
It is shown that Bessel capacities in reflexive Orlicz spaces are non increasing under orthogonal projection of sets. This is used to get a continuity of potentials on some subspaces. The obtained results generalize those of Meyers and Reshetnyak in the case of Lebesgue classes.
On the continuity of quotient multipliers
On the Continuity of Semi-Norms on Operator Algebras.
On the continuity of strongly nonlinear potential
On the continuity of the semivariation in locally convex spaces
On the contracted -algebra of a polycyclic monoid.