Related papers: Lipschitz slices versus linear slices in Banach sp…
We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of $\mathcal{L}_{p}$-spaces. We use…
In this work we provide a characterization of distinct type of (linear and non-linear) maps between Banach spaces in terms of the differentiability of certain class of Lipschitz functions. Our results are stated in an abstract bornological…
This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a…
We present an overview to the approximation property, paying especial attention to the recent results relating the approximation property to ideals of linear operators and Lipschitz ideals. We complete the paper with some new results on…
We show that every Banach space containing isomorphic copies of $c_0$ can be equivalently renormed so that every nonempty relatively weakly open subset of its unit ball has diameter 2 and, however, its unit ball still contains convex…
Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, e.g., as lengths of catheti of right-angled triangles (defined via so-called quasi-orthogonality). These…
The study of the Banach-Saks property in Banach spaces has a long and illustrious history. Of late, motivated by applications in financial mathematics, interest has arisen in the Banach-Saks type properties with respect to order…
In this paper we show the weak Banach-Saks property of the Banach vector space $(L_\mu^p)^m$ generated by $m$ $L_\mu^p$-spaces for $1\leq p<+\infty,$ where $m$ is any given natural number. When $m=1,$ this is the famous Banach-Saks-Szlenk…
In contrast to the usual Lipschitz seminorms associated to ordinary metrics on compact spaces, we show by examples that Lipschitz seminorms on possibly non-commutative compact spaces are usually not determined by the restriction of the…
We study Banach spaces with a weak stable unit ball, that is Banach spaces where every convex combination of relatively weakly open subsets in its unit ball is again a relatively weakly open subset in its unit ball. It is proved that the…
A Banach space has the Schur property when every weakly convergent sequence converges in norm. We prove a Schur-like property for measures: if a sequence of finite signed Borel measures on a Polish space is such that it is bounded in total…
We show that several spaces of holomorphic functions on a Riemann domain over a Banach space, including the nuclear and Hilbert-Schmidt bounded type, are locally $m$-convex Fr\'echet algebras. We prove that the spectrum of these algebras…
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…
We study when diameter two properties pass down to subspaces. We obtain that the slice two property (respectively diameter two property, strong diameter two property) passes down from a Banach space $X$ to a subspace $Y$ whenever $Y$ is…
We consider holomorphic semicocycles on the open unit ball in a Banach space taking values in a Banach algebra. We establish criteria for a semicocycle to be linearizable, that is, cohomologically equivalent to one independent of the…
We study the class of Banach lattices that are positively polynomially Schur. Plenty of examples and counterexamples are provided, lattice properties of this class are proved, arbitrary $L_p(\mu)$-spaces are shown to be positively…
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 study two types of approximations of Lipschitz maps with derivatives of maximal slopes on Banach spaces. First, we characterize the Radon-Nikod\'ym property in terms of strongly norm attaining Lipschitz maps and maximal derivative…
In this work, we establish regularity results for minimizers of the energy functional associated with the thin obstacle problem in Orlicz spaces. More precisely, we prove the Lipschitz continuity and the H\"older continuity of the gradient…
Andreu et al [2] and Sadovskii [11] used representation spaces to study measures of non-compactness and spectral radii of operators on Banach lattices. In this paper, we develop representation spaces based on the nonstandard hull…