On extending and lifting continuous linear mappings in topological vector spaces
On extensions of orthosymmetric lattice bimorphisms
In the paper we prove that every orthosymmetric lattice bilinear map on the cartesian product of a vector lattice with itself can be extended to an orthosymmetric lattice bilinear map on the cartesian product of the Dedekind completion with itself. The main tool used in our proof is the technique associated with extension to a vector subspace generated by adjoining one element. As an application, we prove that if is a commutative -algebra and its Dedekind completion, then, can be equipped...
On extensions of uniformly continuous Banach-space-valued mappings
On Farkas-type theorems
On final topologies.
On Fixed Point Theorems of Maia Type
On generalized paranormed statistically convergent sequence spaces defined by Orlicz function.
On generalized topological spaces I
We begin a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings. We reformulate the axioms. Generalized topology is found to be connected with the concept of a bornological universe. Both GTS and its full subcategory SS of small spaces are topological categories. The second part of this paper will also appear in this journal.
On generalized topological spaces II
This is the second part of A. Piękosz [Ann. Polon. Math. 107 (2013), 217-241]. The categories GTS(M), with M a non-empty set, are shown to be topological. Several related categories are proved to be finitely complete. Locally small and nice weakly small spaces can be described using certain sublattices of power sets. Some important elements of the theory of locally definable and weakly definable spaces are reconstructed in a wide context of structures with topologies.
On Global Central Decomposition for a Universal Cap.
On Grothendieck space ideals.
On Hardy's inequality and eigenvalue distributions
On holomorphic Hahn-Banach extension theorem and properties of bounding and weakly-bounding sets in some metric vector spaces
On homomorphisms, open operators and their adjoints.
On I-convergence of double sequences in the topology induced by random 2-norms
On ideals of operators and of locally convex spaces.
On inclusion relations between Lorentz sequence spaces and inequalities of Lewis type.
On independent sequences in topological linear spaces
On Inductive Limits of Banach Spaces.
On integrability in F-spaces
Some usual and unusual properties of the Riemann integral for functions x : [a,b] → X where X is an F-space are investigated. In particular, a continuous integrable -valued function (0 < p < 1) with non-differentiable integral function is constructed. For some class of quasi-Banach spaces X it is proved that the set of all X-valued functions with zero derivative is dense in the space of all continuous functions, and for any two continuous functions x and y there is a sequence of differentiable...