Related papers: On representing and absolutely representing system…
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 derive a necessary and sufficient condition for the existence of symmetric space structures on quotients of Banach symmetric spaces. Along the way, we investigate the different kinds of reflection subspaces and their Lie triple systems.
Absolutely representing system (ARS) in a Banach space $X$ is a set $D \subset X$ such that every vector $x$ in $X$ admits a representation by an absolutely convergent series $x = \sum_i a_i x_i$ with $(a_i)$ reals and $(x_i) \subset D$. We…
We introduce and study the notion of overcomplete set in a Banach space, that subsumes and extends the classical concept of overcomplete sequence in a (separable) Banach space. We give existence and non-existence results of overcomplete…
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
In this paper we study properties of complete sets and of completions of sets in Banach spaces. We consider the family of completions of a given set and its size; we also study in detail the relationships concerning diameters, radii, and…
Necessary and sufficient conditions for Banach space to be(isometrically isomorphic to) a dual space will be given.
In this series of papers we study subspaces of de Branges spaces of entire functions which are generated by majorization on subsets $D$ of the closed upper half-plane. The present, first, part is addressed to the question which subspaces of…
We construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete $\ks$. We also investigate some interesting properties of…
We show that complemented subspaces of uncountable products of Banach spaces are products of complemented subspaces of countable subproducts.
A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if $E_0$ does not reduce to…
We show that every Banach space saturated with subsymmetric sequences contains a minimal subspace.
A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the…
Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…
We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness…
We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces
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…
The complemented subspace problem asks, in general, which closed subspaces $M$ of a Banach space $X$ are complemented; i.e. there exists a closed subspace $N$ of $X$ such that $X=M\oplus N$? This problem is in the heart of the theory of…
Necessary and sufficient conditions for a separable Banach space to be a dual space are proved. Some applications are discussed
We prove several abstract results giving general conditions under which subspaces of linear or multilinear operators on Banach spaces or Banach lattices are closed. Each of these abstract results is followed by concrete applications,…