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Necessary and sufficient conditions for a separable Banach space to be a dual space are proved. Some applications are discussed

A Banach space E is c_0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c_0. A c_0-saturated Banach space with an unconditional basis which has a quotient space isomorphic to l^2 is constructed.

A Banach space is said to have the ball-covering property (BCP) if its unit sphere can be covered by countably many closed or open balls off the origin. Let $X$ be a Banach space with a shrinking $1$-unconditional basis. In this paper, by…

We will introduce the countable separation property (CSP) of Banach spaces X, which is defined as follows: For each subset \mathcal{F} of X^{\ast}, which separates X, there exists a countable separating subset \mathcal{F}_{0} of…

Blind deconvolution (BD), the resolution of a signal and a filter given their convolution, arises in many applications. Without further constraints, BD is ill-posed. In practice, subspace or sparsity constraints have been imposed to reduce…

It is shown that every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive Indecomposable space.…

A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are…

We provide a sufficient condition for the sum of a finite number of complemented subspaces of a Banach space to be complemented. Under this condition a formula for a projection onto the sum is given. We also show that the condition is sharp…

We show that for every separable Banach space $X$, either $\spw(X)$ (the set of all spreading models of $X$ generated by weakly-null sequences in $X$, modulo equivalence) is countable, or $\spw(X)$ contains an antichain of the size of the…

An increasing sequence of positive integers $(n_k)_{k\ge 0}$ is said to be a Jamison sequence if the following property holds true: for every separable complex Banach space $X$ and every $T\in \mathcal{B}(X)$ which is partially…

Here we give a necessary and sufficient condition for a Banach space to be separable.

The paper explores the correspondence between balanced incomplete block designs (BIBD) and certain linear CNF formulas by identifying the points of a block design with the clauses of the Boolean formula and blocks with Boolean variables.…

Concentration compactness method is a powerful techniques for establishing existence of minimizers for inequalities and of critical points of functionals in general. The paper gives a functional-analytic formulation for the method in Banach…

If a Banach space has an unconditional basis it either contains a continuum of non isomorphic subspaces or is isomorphic to its square and hyperplanes and satisfies other regularity properties. An HI Banach space contains a continuum of non…

Space-Time block codes (STBC) from Orthogonal Designs (OD) and Co-ordinate Interleaved Orthogonal Designs (CIOD) have been attracting wider attention due to their amenability for fast (single-symbol) ML decoding, and full-rate with…

An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree $\mathcal T$ of a certain type on a space X is…

We show that if $X$ and $Y$ are Banach spaces, where $Y$ is separable and polyhedral, and if $T:X \to Y$ is a bounded linear operator such that $T^*(Y^*)$ contains a boundary $B$ of $X$, then $X$ is separable and isomorphic to a polyhedral…

In this paper, we propose an efficient reliability based segmentation-discarding decoding (SDD) algorithm for short block-length codes. A novel segmentation-discarding technique is proposed along with the stopping rule to significantly…

A separable Banach space X contains $\ell_1$ isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded wc_0^*-biorthogonal…

Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach space isomorphic to a subspace of $X^*$. The paper is devoted to the following questions: 1. Under what conditions does there exist an isomorphic embedding $T:Y\to…