Some geometric inequalities in a new Banach sequence space.
Some geometric properties of a generalized Cesàro sequence space.
Some geometric properties of sequence spaces involving lacunary sequence.
Some -type new sequence spaces and their geometric properties.
Some properties of Banach-valued sequence spaces .
Some properties of spaces.
Some results on packing in Orlicz sequence spaces
We present monotonicity theorems for index functions of N-fuctions, and obtain formulas for exact values of packing constants. In particular, we show that the Orlicz sequence space generated by the N-function N(v) = (1+|v|)ln(1+|v|) - |v| with Luxemburg norm has the Kottman constant , which answers M. M. Rao and Z. D. Ren’s [8] problem.
Some topological and geometrical properties of a new difference sequence space.
Stability in vector valued -spaces
Strictly contractive projections on classical sequence spaces
Strongly exposed points in Musielak-Orlicz sequence spaces endowed with Orlicz norm
A criterion for strongly exposed points of the unit ball in Musielak-Orlicz sequence spaces equipped with Orlicz norm is given.
Superposition operator on the space of sequences almost converging to zero
We study the superposition operator f on on the space ac 0 of sequences almost converging to zero. Conditions are derived for which f has a representation of the form f x = a+bx +g x, for all x ∈ ac 0 with a = f 0, b ∈ D(ac 0), g a superposition operator from ℓ∞ into I(ac 0), D(ac 0) = {z: zx ∈ ac 0 for all x ∈ ac 0}, and I(ac 0) the maximal ideal in ac 0. If f is generated by a function f of a real variable, then f is linear. We consider the conditions for which a bounded function f generates f...
Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm
Support functionals in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm are completely characterized. An explicit formula for regular support functionals is given. For obtaining a characterization of singular support functionals a generalized Banach limit is applied. Some necessary and sufficient conditions for smooothness of these spaces are given, too.
The characteristic of weak convergence on Banach sequence lattices.
A sufficient and necessary condition for weak convergence of sequences in a class of Banach sequence lattices is obtained. As a direct application, a complete criterion of a weak convergence of sequences in l infinity is formulated.
The fixed point property in Musielak-Orlicz sequence spaces
In this paper, we give necessary and sufficient conditions for a point in a Musielak-Orlicz sequence space equipped with the Orlicz norm to be an H-point. We give necessary and sufficient conditions for a Musielak-Orlicz sequence space equipped with the Orlicz norm to have the Kadec-Klee property, the uniform Kadec-Klee property and to be nearly uniformly convex. We show that a Musielak-Orlicz sequence space equipped with the Orlicz norm has the fixed point property if and only if it is reflexive....
The Fourier transofrm technique for convolution equations in infinite dimensional lq-spaces.
The Hahn sequence space. III.
The lattice copies of in Banach lattices
It is known that a Banach lattice with order continuous norm contains a copy of if and only if it contains a lattice copy of . The purpose of this note is to present a more direct proof of this useful fact, which extends a similar theorem due to R.C. James for Banach spaces with unconditional bases, and complements the - and -cases considered by Lozanovskii, Mekler and Meyer-Nieberg.
The locally uniform nonsquare in generalized Cesàro sequence spaces.
The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of
Let (S, ∑, m) be any atomless finite measure space, and X any Banach space containing a copy of . Then the Bochner space is uncomplemented in ccabv(∑,m;X), the Banach space of all m-continuous vector measures that are of bounded variation and have a relatively compact range; and ccabv(∑,m;X) is uncomplemented in cabv(∑,m;X). It is conjectured that this should generalize to all Banach spaces X without the Radon-Nikodym property.