Related papers: Banach spaces and Ramsey Theory: some open problem…
Several basic properties of the Drazin spectrum in Banach algebras will be studied. As an application, some results on meromorphic Banach space operators will be obtained.
In this paper we survey some recent works that take the first steps toward establishing bilateral connections between symplectic geometry and several other fields, namely, asymptotic geometric analysis, classical convex geometry, and the…
We survey some principal results and open problems related to colorings of algebraic and geometric objects endowed with symmetries.
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…
In the nonlinear geometry of Banach spaces where the objects in the category are Banach spaces as in the linear case, the morphisms in the new setting are taken to comprise of certain nonlinear maps involving say, Lipschitz maps and, in…
Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman topology and…
In this paper, we show that several extension of Banach contraction principle, can be easily derived from the Caristi's theorem is one of the useful generalization of Banach contraction principle in the setting of the complete metric…
We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold…
There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern exposition of the subtle differences between key results and…
We introduce the embedded Nash problem allowing singularities in the ambient space, and solve it in the case of surfaces, generalizing \cite[Theorem 1.22]{BdlB}.
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.
In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks…
The purpose of the current paper is to introduce some new methods for studying the $p$-adic Banach spaces introduced by Emerton \cite{emerton}. We first relate these spaces to more familiar sheaf cohomology groups. As an application, we…
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.
Several open questions are discussed. The topics include cohomology of current and related Lie algebras, algebras represented as the sum of subalgebras, structures and phenomena peculiar to characteristic $2$, and variations on themes of…
We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented…
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
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…
For a certain class of algebras $\cal A$ we give a method for constructing Banach spaces $X$ such that every operator on $X$ is close to an operator in $\cal A$. This is used to produce spaces with a small amount of structure. We present…