Related papers: On the transfinite symmetric strong diameter two p…

The aim of this note is to study octahedrality in vector valued Lipschitz-free Banach spaces on a metric space under topological hypotheses on it. As a consequence, we get that the space of Lipschitz functions on a metric space valued in a…

We prove that in Lipschitz-free spaces the strong diameter two property, the diameter two property, and the local diameter two property coincide with their corresponding attaining variants.

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…

A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the…

In this paper we study conditions on a Banach space X that ensure that the Banach algebra K(X) of compact operators is amenable. We give a symmetrized approximation property of X which is proved to be such a condition. This property is…

This article aims to examine the Hahn-Banach smoothness of Banach spaces and its connections to various geometrical aspects. We examine the circumstances that allow linear functionals to have unique norm-preserving extensions, with…

We show that finite dimensional Banach spaces fail to be uniformly non locally almost square. Moreover, we construct an equivalent almost square bidual norm on $\ell_\infty.$ As a consequence we get that every dual Banach space containing…

We prove that SL(3,R) has Strong Banach property (T) in Lafforgue's sense with respect to the Banach spaces that are $\theta>0$ interpolation spaces (for the complex interpolation method) between an arbitrary Banach space and a Banach space…

In this paper we survey known results of characterizations of reflexive Banach spaces, which are based on convergence of usual and generalized arithmetic mean (or Ces\`aro sum), weakly compact subsets, affine sets in a Banach space or its…

We introduce and study Banach spaces which have property CWO, i.e., every finite convex combination of relatively weakly open subsets of their unit ball is open in the relative weak topology of the unit ball. Stability results of such…

We characterize the positive Schur property in the positive projective tensor products of Banach lattices, we establish the connection with the weak operator topology and we give necessary and sufficient conditions for the space of regular…

In this paper Hilbert spaces are characterized among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical here: If X is a real Banach space…

In this article, we study the Daugavet property and the diametral diameter two properties in complex Banach spaces. The characterizations for both Daugavet and $\Delta$-points are revisited in the context of complex Banach spaces. We also…

A Banach space has the weak fixed point property if its dual space has a weak$^*$ sequentially compact unit ball and the dual space satisfies the weak$^*$ uniform Kadec-Klee property; and it has the \fpp if there exists $\epsilon>0$ such…

Several characterizations of weak cotype 2 and weak Hilbert spaces are given in terms of basis constants and other structural invariants of Banach spaces. For finite-dimensional spaces, characterizations depending on subspaces of fixed…

We give two examples of polyhedral Banach spaces failing all the diameter two properties, showing that there is not any connection between polyhedrality and the diameter two properties.

We show that all the symmetric projective tensor products of a Banach space $X$ have the Daugavet property provided $X$ has the Daugavet property and either $X$ is an $L_1$-predual (i.e.\ $X^*$ is isometric to an $L_1$-space) or $X$ is a…

In this work we investigate the c_0-extension property. This property generalizes Sobczyk's theorem in the context of nonseparable Banach spaces. We prove that a sufficient condition for a Banach space to have this property is that its…

It is shown that a separable Banach space $X$ can be given an equivalent norm $|\!|\!|\cdot |\!|\!|$ with the following properties:\quad If $(x_n)\subseteq X$ is relatively weakly compact and $\lim_{m\to\infty} \lim_{n\to\infty}\break…

Let X be an L1-predual and E,F be Banach spaces. We use the fact that an unconditionally converging operator T from the injective tensor product of X and E to F is strongly bounded and extend T to an operator S on continuous F-valued…