On the exact value of Jung constants of Orlicz sequence spaces.
On the existence of a fundamental total and bounded biorthogonal sequence in every separable Banach space, and related constructions of uniformly bounded orthonormal systems in L²
On the existence of almost greedy bases in Banach spaces
We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedy bases begun in [3]. We show that almost greedy bases are essentially optimal for n-term approximation when the TGA is modified to include a Chebyshev approximation. We prove that if a Banach space X has a basis and contains a complemented subspace with a symmetric basis and finite cotype then X has an...
On the existence of distinguished bases in a -space
On the existence of fundamental and total founded biorthogonal systems in Banach spaces
On the existence of non-linear frames
A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if is a Banach space such that has a SRBF, then has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space has an approximative Schauder frame, then has a SRBF. Finally, the existence of a non-linear SRBF in the conjugate of a separable Banach space has been proved.
On the existence of Schauder bases in Sobolev spaces
On the Extension of Continuous Linear Functionals and Best Approximation in Normed Linear Spaces.
On the extension of rotund norms.
On the extremal points of the closed unit balls in some abstract spaces
On the Extreme Points and Strongly Extreme Points in Köther-Bochner Spaces
On the Facial Structure of the Unit Ball of a GM-Space.
On the Fejér means of bounded Ciesielski systems
We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space to if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n...
On the fixed point property in direct sums of Banach spaces with strictly monotone norms
It is shown that if a Banach space X has the weak Banach-Saks property and the weak fixed point property for nonexpansive mappings and Y has the asymptotic (P) property (which is weaker than the condition WCS(Y) > 1), then X ⊕ Y endowed with a strictly monotone norm enjoys the weak fixed point property. The same conclusion is valid if X admits a 1-unconditional basis.
On the fixed points of nonexpansive mappings in direct sums of Banach spaces
We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum X ⊕ Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.
On the fixed-point property of unital uniformly closed subalgebras of .
On the frame of the unit ball of Banach spaces
The notion of the frame of the unit ball of Banach spaces was introduced to construct a new calculation method for the Dunkl-Williams constant. In this paper, we characterize the frame of the unit ball by using k-extreme points and extreme points of the unit ball of two-dimensional subspaces. Furthermore, we show that the frame of the unit ball is always closed, and is connected if the dimension of the space is not less than three. As infinite dimensional examples, the frame of the unit balls of...
On the Fréchet differentiability of distance functions
On the Gelfand-Philips Property in ?-tensor Products.
On the Gelfand-Phillips property in Banach spaces with PRI.