Related papers: Asymptotically symmetric spaces with hereditarily …

For every $n\geq 3,$ we construct an $n$-dimensional Banach space which is isometric to a subspace of $L_{1/2}$ but is not isometric to a subspace of $L_1.$ The isomorphic version of this problem (posed by S. Kwapien in 1969) is still open.…

The main purpose of this paper is to introduce the notion of an asymptotically almost periodic ultradistribution and asymptotically almost automorphic ultradistribution with values in a Banach space, as well as to further analyze the…

We study the superspace formulation of the noncommutative nonlinear supersymmetric O(N) invariant sigma-model in 2+1 dimensions. We prove that the model is renormalizable to all orders of 1/N and explicitly verify that the model is…

We present a new approach to the theory of asymptotic properties of solutions of difference equations. Usually, two sequences $x,y$ are called asymptotically equivalent if the sequence $x-y$ is convergent to zero i.e., $x-y\in c_0$, where…

Let $X$ be a completely regular space. For a non-vanishing self-adjoint Banach subalgebra $H$ of $C_B(X)$ which has local units we construct the spectrum $\mathfrak{sp}(H)$ of $H$ as an open subspace of the Stone-Cech compactification of…

In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence…

We give biorthogonal system characterizations of Banach spaces that fail the Dunford-Pettis property, contain an isomorphic copy of $c_0$, or fail the hereditary Dunford-Pettis property. We combine this with previous results to show that…

A Banach space is {\it polynomially Schur} if sequential convergence against analytic polynomials implies norm convergence. Carne, Cole and Gamelin show that a space has this property and the Dunford-Pettis property if and only if it is…

For a Banach space $X$, we show that any family of graphs quasi-isometric to levels of a warped cone $\mathcal O_\Gamma Y$ is an expander with respect to $X$ if and only if the induced $\Gamma$-representation on $L^2(Y;X)$ has a spectral…

We introduce a flexible almost isometric version of the almost transitivity property of Banach spaces. With the help of this new notion we generalize to several directions a strong recent rotational characterization of Hilbert spaces due to…

We continue the study of Uniformly Finitely Extensible Banach spaces (in short, UFO) initiated in Moreno-Plichko, \emph{On automorphic Banach spaces}, Israel J. Math. 169 (2009) 29--45 and Castillo-Plichko, \emph{Banach spaces in various…

We investigate asymptotic symmetries in flat backgrounds of dimension higher than or equal to four. For spin two we provide the counterpart of the extended BMS transformations found by Campiglia and Laddha in four-dimensional Minkowski…

In this paper, we present some common fixed point theorems for a commuting pair of mappings, including a generalized nonexpansive single valued mapping and a generalized nonexpansive multivalued mapping in strictly convex Banach spaces. The…

The purpose of this article is to generalize some known characterizations of Banach space properties in terms of graph preclusion. In particular, it is shown that superreflexivity can be characterized by the non-equi-bi-Lipschitz…

A subset of a Banach space is called equilateral if the distances between any two of its distinct elements are the same. It is proved that there exist non-separable Banach spaces (in fact of density continuum) with no infinite equilateral…

We introduce and study the notion of space of almost universal complemented disposition (a.u.c.d.) as a generalization of Kadec space. We show that every Banach space with separable dual is isometrically contained as a $1$-complemented…

We provide a short characterization of $p$-asymptotic uniform smoothability and asymptotic uniform flatenability of operators and of Banach spaces. We use these characterizations to show that many asymptotic uniform smoothness properties…

We study the relations between different notions of almost locally uniformly rotund points that appear in literature. We show that every non-reflexive Banach space admits an equivalent norm having a point in the corresponding unit sphere…

Let $1\le p<\infty$. A symmetric space $X$ on $[0,1]$ is said to be $p$-disjointly homogeneous (resp. restricted $p$-disjointly homogeneous) if every sequence of normalized pairwise disjoint functions from $X$ (resp. characteristic…

Given a map $f \colon E \longrightarrow F$ between Banach spaces (or Banach lattices), a set $A$ of $E$-valued bounded sequences, ${\bf x} \in A$ and a vector topology $\tau$ on $F$, we investigate the existence of an infinite dimensional…