Related papers: Daugavet property and separability in Banach space…

We introduce and analyse the notion of slice continuity between operators on Banach spaces in the setting of the Daugavet property. It is shown that under the slice continuity assumption the Daugavet equation holds for weakly compact…

The aim of this note is to consider different notions for the Banach-Saks property in locally solid vector lattices as an extension for the known concepts of the Banach-Saks property in Banach lattices. We investigate relations between…

We show that $W^{1,1}(\mathbb{R}^2)$ has the Daugavet property when endowed with the norm induced by the $L^1$-norm of the gradient, but fails to have the slice diameter two property when equipped with the usual Sobolev norm.

Several new characterizations of Banach spaces containing a subspace isomorphic to $\ell^1$, are obtained. These are applied to the question of when $\ell^1$ embeds in the injective tensor product of two Banach spaces.

We continue the investigation of the behaviour of octahedral norms in tensor products of Banach spaces. Firstly, we will prove the existence of a Banach space $Y$ such that the injective tensor products $l_1\widehat{\otimes}_\varepsilon Y$…

The paper is a complement to the survey: M.I.Ostrovskii "To\-po\-lo\-gies on the set of all subspaces of a Banach space and related questions of Banach space geometry", Quaestiones Math. (to appear). It contains proofs of some results on…

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…

We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This…

We show that for a Banach algebra $A$ with a bounded approximate identity, the amenability of the projective tensor product of A with A, the amenability of the projective tensor product of A with A^{op}and the amenability of A are…

In this article, we study the relationship between \(p\)-\((V)\) subsets and p-\(V^*\) subsets of dual spaces. We investigate the Banach space X with the property that adjoint every \(p\)-convergent operator \(T: X \rightarrow Y\) is weakly…

It is shown that if the dual of a separable Banach space has Property($K^*$) then the original space has the weak fixed point property. This is an improvement of previously results.

Character inner amenability for certain class of Banach algebras consist of projective tensor product $A\hat{\otimes}B$, Lau product $A\times_\theta B$ and module extension $A\oplus X$ are investigated. Some illuminating examples are also…

We characterise the weak$^*$ symmetric strong diameter $2$ property in Lipschitz function spaces by a property of its predual, the Lipschitz-free space. We call this new property decomposable octahedrality and study its duality with the…

We discuss relationships in Lindelof spaces among the properties "indestructible", "productive", "D", and related properties.

Heinrich, Mankiewicz, Sims, and Yost proved that every separable subspace of a Banach space $Y$ is contained in a separable ideal in $Y$. We improve this result by replacing the term "ideal" with the term "almost isometric ideal". As a…

This work explores the equivalence of two sequential properties, $D$ and $D'$, for dual Banach spaces under the weak* topology. Property $D$ ensures that any totally scalarly measurable function is also scalarly measurable, while property…

We prove that there exists an equivalent norm $\Vert\vert\cdot\vert\Vert$ on $L_\infty[0,1]$ with the following properties: (1) The unit ball of $(L_\infty[0,1],\Vert\vert\cdot\vert\Vert)$ contains non-empty relatively weakly open subsets…

We introduce extensions of $\Delta$-points and Daugavet points in which slices are replaced by relative weakly open subsets (super $\Delta$-points and super Daugavet points) or by convex combinations of slices (ccs $\Delta$-points and ccs…

We compute the Borel complexity of some classes of Banach spaces such as different versions of diameter two properties, spaces satisfying the Daugavet equation or spaces with an octahedral norm. In most of the above cases our computation is…

We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson's property ($\mathcal{C}$), Talponen's Countable Separation Property, or being a G\^ateaux…