On the surjective Dunford-Pettis property
On the tensor product weakly compact operators.
On the "Three space problem".
On the three-space property: non-containment of lp, 1 ≤ p < ∞, or c0 subspaces.
The main result in this paper is the following: Let E be a Fréchet space having a normable subspace X isomorphic to lp, 1 ≤ p < ∞, or to c0. Let F be a closed subspace of E. Then either F or E/F has a subspace isomorphic to X.
On the type constants with respect to systems of characters of a compact abelian group
We prove that there exists an absolute constant c such that for any positive integer n and any system Φ of characters of a compact abelian group, , where T is an arbitrary operator between Banach spaces, is the type norm of T with respect to Φ and is the usual Rademacher type-2 norm computed with n vectors. For the system of the first Walsh functions this is even true with c=1. This result combined with known properties of such type norms provides easy access to quantitative versions of...
On the uncomplemented subspace
On the uniform convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm
In [5], we characterized the uniform convexity with respect to the Luxemburg norm of the Besicovitch-Orlicz space of almost periodic functions. Here we give an analogous result when this space is endowed with the Orlicz norm.
On the uniformly normal structure of Orlicz spaces with Orlicz norm
We prove that in Orlicz spaces endowed with Orlicz norm the uniformly normal structure is equivalent to the reflexivity.
On the upper envelopes of a family of -disjoint operators.
On the volume method in the study of Auerbach bases of finite-dimensional normed spaces
In this note we show that if the ratio of the minimal volume V of n-dimensional parallelepipeds containing the unit ball of an n-dimensional real normed space X to the maximal volume v of n-dimensional crosspolytopes inscribed in this ball is equal to n!, then the relation of orthogonality in X is symmetric. Hence we deduce the following properties: (i) if V/v=n! and if n>2, then X is an inner product space; (ii) in every finite-dimensional normed space there exist at least two different Auerbach...
On the volume of unit balls in Banach spaces
On the weak amenability of ℬ(X)
We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.
On the weak star uniformly rotund points of Orlicz spaces.
We obtain the necessary and sufficient condition of weak star uniformly rotund point in Orlicz spaces.
On the weak uniform rotundity of Banach spaces.
On the weak-basis theorem
On the WM points of Orlicz function spaces endowed with Luxemburg norm.
The concept of WM point is introduced and the criterion of WM property in Orlicz function spaces endowed with Luxemburg norm is given.
On the WM points of Orlicz function spaces endowed with Orlicz norm.
In this paper, we introduce the concept of WM point and obtain the criterion of WM points for Orlicz function spaces endowed with Orlicz norm and the criterion of WM property for Orlicz space.
On the WM property of Orlicz sequence spaces endowed with the Orlicz norm
We obtain the criterion of the WM property for Orlicz sequence spaces endowed with the Orlicz norm.
On the “zero-two” law for positive contractions in the Banach-Kantorovich lattice
In the present paper we prove the “zero-two” law for positive contractions in the Banach-Kantorovich lattices , constructed by a measure with values in the ring of all measurable functions.
On the λ-property and spaces of convergent sequences.