Rearrangement of series in nonnuclear spaces
It is proved that if a metrizable locally convex space is not nuclear, then it does not satisfy the Lévy-Steinitz theorem on rearrangement of series.
Reflexivität und Schauder Basen vom Typ P und P in lokalkonvexen Räumen.
Regular methods of summability in some locally convex spaces
Suppose that is a Fréchet space, is a regular method of summability and is a bounded sequence in . We prove that there exists a subsequence of such that: either (a) all the subsequences of are summable to a common limit with respect to ; or (b) no subsequence of is summable with respect to . This result generalizes the Erdös-Magidor theorem which refers to summability of bounded sequences in Banach spaces. We also show that two analogous results for some -locally convex spaces...
Relationship between Order Completeness and Topological Completeness.
Remarks on bases in a Fréchet function space.
Remarks on the existence of unconditional bases for weighted countably-Hilbert spaces and their complemented subspaces.
Renormalized solutions for nonlinear degenerate elliptic problems with L1 data.
Representing and absolutely representing systems
We introduce various classes of representing systems in linear topological spaces and investigate their connections in spaces with different topological properties. Let us cite a typical result of the paper. If H is a weakly separated sequentially separable linear topological space then there is a representing system in H which is not absolutely representing.
R-Schauder decompositions. Some applications.
Schauder bases and reflexivity
Schauder decompositions and their applications to continuity of maps.
Schauder decompositions in dual and bidual spaces
Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals.
Sequence space representations for (FN)-algebras of entire functions modulo closed ideals
Sequence space representations for zero-solutions of convolution equations on ultradifferentiable functions of Roumieu type
Sequence spaces and interpolation problems for analytic functions
Sequences of 0's and 1's
We investigate the extent to which sequence spaces are determined by the sequences of 0's and 1's that they contain.
Sequences of 0's and 1's: sequence spaces with the separable Hahn property
In [3] it was discovered that one of the main results in [1] (Theorem 5.2), applied to three spaces, contains a nontrivial gap in the argument, but neither the gap was closed nor a counterexample was provided. In [4] the authors verified that all three above mentioned applications of the theorem are true and stated a problem concerning the topological structure of one of these three spaces. In this paper we answer the problem and give a counterexample to the theorem in doubt. Also we establish a...
Several notions of absolute bases.
Sobre sumabilidad Cesáro en el espacio CS (I).