Some estimates for the weakly convergent sequence coefficient in Banach spaces

Some Estimates on the Weakly Convergent Sequence Coefficient in Banach Spaces

In this paper, we study the weakly convergent sequence coefficient and obtain its estimates for some parameters in Banach spaces, which give some sufficient conditions for a Banach space to have normal structure.

Some Inequalities Concerning the Weakly Convergent Sequence Coefficient in Banach Spaces

Weakly Convergent Sequence Coefficient of Product Space

W. L. Bynum introduced the weakly convergent sequence coefficient WCS(A') of the Banach space X as WCS(Jf) = sup{M: for each weakly convergent sequence {xn} in X , there is some y e co({x«}) such that M • lim sup ||x,, y\\ < A({x„})} . We consider the weakly convergent sequence coefficient of the /^-product space Z = (fTjLi Xi)t of tne finite non-Schur space Xx, ... , X„ and show that WCS(Z) = ...

Coefficient Quantization in Banach Spaces

Let (ei) be a dictionary for a separable Banach space X . We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a ‘finite alphabet’. We investigate several approximation properties of this type and connect them to the Banach space geometry of X . The existence of a total minimal system with one of these properties, ...

Coefficient Quantization for Frames in Banach Spaces

Let (ei) be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are possibly redundant. Our model for this situation will be frames in Banach spaces.