Related papers: Absolutely representing systems, uniform smoothnes…

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.

An absolutely representing family of subspaces is a natural generalization of an absolutely representing system of subspaces and absolutely representing system (of elements). We obtain necessary an (or) sufficient conditions for a family of…

We show by a ridiculously simple argument that, for any norm on the tensor product of vector spaces, every element of the completion can be represented as a convergent series of elementary tensors.

Answering one problem that has its origins in quantum mechanics, we prove that for any sequence $(A_n)_{n\in\mathbb N}$ of convex nowhere dense sets in a Banach space $X$ and any sequence $(\varepsilon_n)_{n=1}^\infty$ of positive real…

This work deals with a maximal monotone operator $A$ of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value $Ax$ at a given point $x$ via its values at nearby points of $x$. We…

We study the notions of acs, luacs and uacs Banach spaces which were introduced by V. Kadets et al. in 2000 and form common generalisations of the usual rotundity and smoothness properties of Banach spaces. In particular, we are interested…

We study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For $n\ge 2$ and $1<p<\infty$, it is shown that $\ell_\infty^n$ is representable in a Banach space $X$ if and only if it…

In this paper, we first show that for a Banach space $X$ there is a fully order reversing mapping $T$ from ${\rm conv}(X)$ (the cone of all extended real-valued lower semicontinuous proper convex functions defined on $X$) onto itself if and…

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 construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…

A Banach space X is superreflexive if each Banach space Y that is finitely representable in X is reflexive. Superreflexivity is known to be equivalent to J-convexity and to the non-existence of uniformly bounded factorizations of the…

A survey is given of the work on strong regularity for uniform algebras over the last thirty years, and some new results are proved, including the following. Let A be a uniform algebra on a compact space X and let E be the set of all those…

In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an $M$-ideal in the space of bounded operators, a very smooth operator $T$ attains…

In the article is introduced a new class of Banach spaces that are called sub B-convex. Namely, a Banach space X is said to be B -convex if it may be represented as a direct sum l_1+ W, where W is B-convex. It will be shown that any…

We address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach…

We provide a few characterizations of a strictly convex Banach space. Using this we improve the main theorem of [Digar, Abhik; Kosuru, G. Sankara Raju; Cyclic uniform Lipschitzian mappings and proximal uniform normal structure. Ann. Funct.…

We single out and study a natural class of Banach spaces -- almost square Banach spaces. In an almost square space we can find, given a finite set $x_1,x_2,\ldots,x_N$ in the unit sphere, a unit vector $y$ such that $\|x_i-y\|$ is almost…

The paper elucidates the relationship between the density of a Banach space and possible sizes of well-separated subsets of its unit sphere. For example, it is proved that for a large enough space $X$, the unit sphere $S_X$ always contains…

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X --> X such that the set A = {x in X : ||R^n(x)|| --> infinity} is non-empty and nowhere dense in X. Moreover, if…

Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…