Related papers: Diametral diameter two properties in Banach spaces

In this short note, we study two different geometrical aspects of Banach spaces with small diameter properties, namely the Ball Dentable Property (BDP), Ball Huskable Property (BHP) and Ball Small Combination of slice Property (BSCSP). We…

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…

The main purpose of the paper is to present some recent results on metric characterizations of superreflexivity and the Radon-Nikod\'ym property.

We provide sufficient conditions for a mapping acting between two Banach spaces to be a diffeomorphism.

Let X be a closed subspace of a Banach space Y and J be the inclusion map. We say that the pair (X,Y) has the Daugavet property if for every rank one bounded linear operator T from X to Y the following equality \|J+T\|=1+\|T\| holds. A new…

The maximal roundness of a metric space is a quantity that arose in the study of embeddings and renormings. In the setting of Banach spaces, it was shown by Enflo that roundness takes on a much simpler form. In this paper we provide simple…

A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…

We study properties of representing and absolutely representing systems of subspaces in Banach spaces. We also present sufficient conditions for the system of subspaces to be a representing system of subspaces.

The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.

A Banach space $X$ is said to have the Daugavet property if every operator $T: X\to X$ of rank~$1$ satisfies $\|Id+T\| = 1+\|T\|$. We show that then every weakly compact operator satisfies this equation as well and that $X$ contains a copy…

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…

A norm one element $x$ of a Banach space is a Daugavet-point (respectively, a $\Delta$-point) if every slice of the unit ball (respectively, every slice of the unit ball containing $x$) contains an element, which is almost at distance 2…

We give a characterisation of the weak* symmetric strong diameter 2 property for Lipschitz function spaces in terms of a property of the corresponding metric space. Using this characterisation we show that the weak* symmetric strong…

We study convexity and starlikeness of quasihyperbolic and distance ratio metric balls on Banach spaces. In particular, problems related to these metrics on convex domains, and on punctured Banach spaces, are considered.

In this short note, we first consider some inequalities for comparison of some algebraic properties of two continuous algebra-multiplications on an arbitrary Banach space and then, as an application, we consider some very basic observations…

The primary objective of this paper is to propose and analyze the notion of dual cones associated with the metric projection and generalized projection in Banach spaces. We show that the dual cones, related to the metric projection and…

We explore the relationship in metric spaces between different properties related to the Besicovitch covering theorem, and also consider weak versions of doubling, in connection to the non-uniqueness of centers and radii in arbitrary metric…

In this paper, a strong variant for multivalued mappings of the well-known property of openness at a linear rate is studied. Among other examples, a simply characterized class of closed convex processes between Banach spaces, which…

A necessary and sufficient condition for existence of a Banach space with a finite dimensional decomposition but without the $\pi$-property in terms of norms of compositions of projections is found.

We provide some new consequences on the Lipschitz numerical radius and index which were introduced recently. More precisely, we give some renorming results on the Lipschitz numerical index, introduce a concept of Lipschitz numerical radius…