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...
Sequences of independent identically distributed functions in rearrangement invariant spaces
A new set of sufficient conditions under which every sequence of independent identically distributed functions from a rearrangement invariant (r.i.) space on [0,1] spans there a Hilbertian subspace are given. We apply these results to resolve open problems of N. L. Carothers and S. L. Dilworth, and of M. Sh. Braverman, concerning such sequences in concrete r.i. spaces.
Sequences or random variables in Lp for p<1.
Sequential closedness of Boolean algebras of projections in Banach spaces
Complete and σ-complete Boolean algebras of projections acting in a Banach space were introduced by W. Bade in the 1950's. A basic fact is that every complete Boolean algebra of projections is necessarily a closed set for the strong operator topology. Here we address the analogous question for σ-complete Boolean algebras: are they always a sequentially closed set for the strong operator topology? For the atomic case the answer is shown to be affirmative. For the general case, we develop criteria...
Sequential compactness for the weak topology of vector measures in certain nuclear spaces.
Sequential completeness and regularityof inductive limits of webbed spaces
Any inductive limit of bornivorously webbed spaces is sequentially complete iff it is regular.
Sequential completeness and spaces with the gliding Humps property.
Sequential completeness of inductive limits.
Sequential completeness of LF-spaces
Any LF-space is sequentially complete iff it is regular.
Sequential convergence in topological vector spaces.
Sequential convergences and Dunford-Pettis properties.
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 density techniques for an approximate Radon–Nikodým theorem.
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 compact sets in a class of generalized Orlicz spaces
In this paper, we will characterize sequentially compact sets in a class of generalized Orlicz spaces.
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.
Sequentially Right Banach spaces of order
We introduce and study two new classes of Banach spaces, the so-called sequentially Right Banach spaces of order , and those defined by the dual property, the sequentially Right Banach spaces of order for . These classes of Banach spaces are characterized by the notions of -limited sets in the corresponding dual space and subsets of the involved Banach space, respectively. In particular, we investigate whether the injective tensor product of a Banach space and a reflexive Banach space...
Series de Dirichlet consideradas como espacios de sucesiones.