Related papers: A separable L-embedded Banach space has property (…

In this paper we present new characterizations of Banach spaces whose duals are isomorphic to $l_{1}(\Gamma),$ extending results of Stegall, Lewis-Stegall and Cilia-D'Anna-Guti\'{e}rrez.

We characterize preduals and K\"othe duals to a class of Sobolev multiplier type spaces. Our results fit in well with the modern theory of function spaces of harmonic analysis and are also applicable to nonlinear partial differential…

Let $E$ be one of the spaces $C(K)$ and $L_1$, $F$ be an arbitrary Banach space, $p>1,$ and $(X,\sigma)$ be a space with a finite measure. We prove that $E$ is isometric to a subspace of the Lebesgue-Bochner space $L_p(X;F)$ only if $E$ is…

Let X and Y be two infinite-dimensional Banach spaces. If X is crudely finitely representable in every finite-codimensional subspace of Y, then any proper subset of X almost bi-Lipschitz embeds into Y, in a sense quite close to that of F.…

It is known that a Banach space has the strong diameter 2 property (i.e. every convex combination of slices of the unit ball has diameter 2) if and only if the norm on its dual space is octahedral (a notion introduced by Godefroy and…

We provide two examples of complex homogeneous quadratic polynomials P on Banach spaces of the form l_1(I). The first polynomial P has both separable and nonseparable maximal zero subspaces. The second polynomial P has the property that…

It is well known that the bidual of $\mathrm C(X)$ for a compact space $X$, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to $\mathrm C(\tilde X)$ for some compact space $\tilde X$. The space $\tilde X$ is…

If a separable Banach space contains an isometric copy of every separable reflexive Fr\'echet smooth Banach space, then it contains an isometric copy of every separable Banach space. The same conclusion holds if we consider separable Banach…

We study the predual of the space of functions of bounded variation defined over a metric measure space $({\rm X},{\sf d},\mathfrak m)$ with $\mathfrak m$ finite. More specifically, for any exponent $p\in(1,\infty)$ we construct an…

Cocompactness is a property of embeddings between two Banach spaces, similar to but weaker than compactness, defined relative to some non-compact group of bijective isometries. In presence of a cocompact embedding, bounded sequences (in the…

We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to…

We show that the predual of a JBW$^*$-triple has the weak Banach-Saks property, that is, reflexive subspaces of a JBW$^*$-triple predual are super-reflexive. We also prove that JBW$^*$-triple preduals satisfy the Koml\'os property (which…

We characterise the class of those Banach spaces in which every convex combination of slices of the unit ball intersects the unit sphere as the class of those spaces in which every convex combination of slices of the unit ball contains two…

We define and study the notion of property $(\rm T)$ for Banach algebras, generalizing the one from $C^*$-algebras. For a second countable locally compact group $G$ and a given family of Banach spaces $\mathcal E$, we prove that our Banach…

In this paper we study two properties viz. property-$U$ and property-$SU$ of a subspace $Y$ of a Banach space which correspond to the uniqueness of the Hahn-Banach extension of each linear functional in $Y^*$ and in addition to that this…

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…

An isomorphic (\ell_1)-predual space (X) is constructed such that neither (X) is isomorphic to a subspace of (c_0), nor (C(\omega^\omega)) is isomorphic to a subspace of (X). It follows that (X) is not isomorphic to a complemented subspace…

In this article, we analyse the structure of finite dimensional subspaces of the set of points of strong subdifferentiability in a dual space. In a dual $L_1(\mu)$ space, such a subspace is in the discrete part of the Yoshida-Hewitt type…

Necessary and sufficient conditions for Banach space to be(isometrically isomorphic to) a dual space will be given.

In this paper, we introduce and study the concept of L-Dunford-Pettis sets and L-Dunford-Pettis property in Banach spaces. Next, we give a characterization of the L-Dunford-Pettis property with respect to some well-known geometric…