Related papers: Diameter two properties and polyhedrality

We give a complete characterization of those $f: [0,1] \to X$ (where $X$ is a Banach space which admits an equivalent Fr\'echet smooth norm) which allow an equivalent $C^2$ parametrization. For $X=\R$, a characterization is well-known.…

In this paper we investigate the property (HLUR), a generalisation of (LUR) property of a Banach space. A Banach space having the property (HLUR) is called an HLUR space. We characterise (HLUR) property with the help of known geometric…

The quotient shape types of normed vectorial spaces(over the same field) with respect to Banach spaces reduce to those of Banach spaces. The finite quotient shape type of normed spaces is an invariant of the (algebraic) dimension, but not…

We study the existence of Daugavet- and delta-points in the unit sphere of Banach spaces with a $1$-unconditional basis. A norm one element $x$ in a Banach space is a Daugavet-point (resp. delta-point) if every element in the unit ball…

A $\Delta$-point $x$ of a Banach space is a norm one element that is arbitrarily close to convex combinations of elements in the unit ball that are almost at distance $2$ from $x$. If, in addition, every point in the unit ball is…

We introduce the Integrated Dual Local Depth which is a local depth measure for data in a Banach space based on the use of one-dimensional projections. The properties of a depth measure are analyzed under this setting and a proper…

A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of…

For a real normed space $X$, we study the $n$-dual space of $\left(X,\left\Vert \cdot \right\Vert \right) $ and show that the space is a Banach space. Meanwhile, for a real normed space $X$ of dimension $d\geq n$ which satisfies property…

We prove that if X is a separable infinite dimensional Banach space then its isomorphism class has infinite diameter with respect to the Banach-Mazur distance. One step in the proof is to show that if X is elastic then X contains an…

This paper explores the dual space corresponding to p-Bergman space and examines the essential condition for the dual space to be a q-Bergman space. The investigation involves a detailed examination of the interpolation space of a Banach…

Inspired by the recent results toward Birkhoff conjecture (a rigidity property of billiards in ellipses), we discuss two rigidity properties of conics. The first one concerns symmetries of an analog of polar duality associated with an oval,…

G. Godefroy asked whether, on any Banach space, the set of norm-attaining functionals contains a 2-dimensional linear subspace. We prove that a recent construction due to C.J. Read provides an example of a space which does not have this…

We give a metric characterisation of when the Lipschitz-free space over a separable ultrametric space is a dual Banach space. In the case where the Lipschitz-free space has a predual, we show that this predual is M-embedded if and only if…

We construct surface measures associated to Gaussian measures in separable Banach spaces, and we prove several properties including an integration by parts formula.

Spaces of homogeneous polynomials on a Banach space are frequently equipped with quasinorms instead of norms. In this paper we develop a technique to replace the original quasi-norm by a norm in a dual preserving way, in the sense that the…

The main result of this article is a rigidity result pertaining to the spreading model structure for Banach spaces coarsely embeddable into Tsirelson's original space $T^*$. Every Banach space that is coarsely embeddable into $T^*$ must be…

The requirement of an $SL(2)$ duality symmetry, mixing the worldvolume field equations with Bianchi identities, leads to a highly nonlinear equation involving the transformation parameters and certain worldvolume currents. In general, this…

We prove that, in dimensions greater than 2, the generic metric is not a Hessian metric and find a curvature condition on Hessian metrics in dimensions greater than 3. In particular we prove that the forms used to define the Pontryagin…

For a large class of Banach spaces, a general construction of subspaces without local unconditional structure is presented. As an application it is shown that every Banach space of finite cotype contains either $l_2$ or a subspace without…

We provide sufficient conditions for a mapping between two Banach spaces to be a diffeomorphism using the approach of an auxiliary functional and also by the aid of a duality mapping corresponding to a normalization function. We simplify…