Related papers: Banach spaces and Ramsey Theory: some open problem…
The notion of a topological Ramsey space was introduced by Carlson some 30 years ago. Studying the topological Ramsey space of variable words, Carlson was able to derive many classical combinatorial results in a unifying manner. For the…
This is the second part in a series dealing with subspaces of de Branges spaces of entire function generated by majorization on subsets of the closed upper half-plane. In this part we investigate certain Banach spaces generated by…
In the paper is considered two problems on extension of operators whose range space for the first problem (or domain space for the second one) belongs to the fixed class of finite equivalence, which is generated by a given Banach space $X$.…
The article is devoted to topological homeomorphisms of Banach spaces over complete non-Archimedean normed infinite fields with products of copies of the fields.
We study uniform and coarse embeddings between Banach spaces and topological groups. A particular focus is put on equivariant embeddings, i.e., continuous cocycles associated to continuous affine isometric actions of topological groups on…
This preprint concerns Banach spaces of functions converging at infinity. In particular, spaces of continuous functions, Lebesgue spaces and sequence spaces. In each framework we show versions of Riesz's representation theorem.
In this paper, we consider some equilibrium problems (or saddle point problems), in which the domains of the considered mappings are limited at some regions. These restricted regions are defined by some mappings which are called the…
This paper is devoted to the study of strongly quasinonexpansive mappings in an abstract space and a Banach space.
We use Birkhoff-James' orthogonality in Banach spaces to provide new conditions for the converse of the classical Riesz's representation theorem.
This paper explores some important aspects of the theory of rearrangement-invariant quasi-Banach function spaces. We focus on two main topics. Firstly, we prove an analogue of the Luxemburg representation theorem for rearrangement-invariant…
This is an attempt to build Banach space valued theory for certain singular integrals on Hamming cube. Of course all estimates below are dimension independent, and we tried to find ultimate sharp assumptions on the Banach space for a…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
On a geometrical view, the conception of map geometries are introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surface. Results convinced one that map geometries are…
We provide sufficient conditions for a mapping acting between two Banach spaces to be a diffeomorphism.
In this paper, using a more generalized inequality instead of triangle inequality, the notion of \theta-metric space is introduced. Some important properties of induced topology by such spaces are presented. Also, Banach and Caristi type…
We obtain some results for and further examples of subprojective and superprojective Banach spaces. We also give several conditions providing examples of non-reflexive superprojective spaces; one of these conditions is stable under…
In this paper, we study the descriptive complexity of some inevitable classes of Banach spaces. Precisely, as shown in [Go], every Banach space either contains a hereditarily indecomposable subspace or an unconditional basis, and, as shown…
A Banach space E is said to have Property (w) if every (bounded linear) operator from E into E' is weakly compact. We give some interesting examples of James type Banach spaces with Property (w). We also consider the passing of Property (w)…
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.
When optimization theorists consider optimization problems in infinite dimensional spaces, they need to deal with closed convex subsets(usually cones) which mostly have empty interior. These subsets often prevent optimization theorists from…