Related papers: A note on the probabilistic N-Banach spaces
These lecture notes contain an introduction to some of the fundamental ideas and results in analysis and probability on infinite-dimensional spaces, mainly Gaussian measures on Banach spaces. They originated as the notes for a topics course…
The idea of best approximation in linear n-normed space is presented and some examples showing various possibilities of best approximations in linear n-normed space is given. Also, we study strictly convex n-norm and enquire about the…
Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.
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 discuss some open problems in the Geometry of Banach spaces having Ramsey-theoretic flavor. The problems are exposed together with well known results related to them.
The aim of this paper is to establish a strong convergence theorem for a strongly nonexpansive sequence in a Banach space. We also deal with some applications of the convergence theorem.
We establish a general criterion for the existence of convex sets of fixed shape as, e.g., balls of a given radius, of maximal probability on Banach spaces. We also provide counterexamples showing that their existence my fail even in some…
We study random unconditional convergence for a basis in a Banach space. The connections between this notion and classical unconditionality are explored. In particular, we analyze duality relations, reflexivity, uniqueness of these bases…
In this paper, we present the classification of generalized Wallach spaces and discuss some related problems.
We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in the previous paper Banach spaces without minimal subspaces, by classifying them according to which side of the…
In this paper, we study several type of point derivations for Banach algebras. We investigate how our definition of point derivations are related to each others.
We completely characterize the left-symmetric points, the right-symmetric points, and, the symmetric points in the sense of Birkhoff-James, in a Banach space. We obtain a complete characterization of the left-symmetric (right-symmetric)…
We collect several open questions in Banach spaces, mostly related to measure theoretic aspects of the theory. The problems are divided into five categories: miscellaneous problems in Banach spaces (non-separable $L^p$ spaces, compactness…
In this survey, we discuss the definition of a (quasi-)Banach function space. We advertise the original definition by Zaanen and Luxemburg, which does not have various issues introduced by other, subsequent definitions. Moreover, we prove…
We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.
Concept of p-frame with the help of b-linear functional in the case of n-Banach space is being presented and its few properties, one of them, Cartesian product of two p-frames again becomes a p-frame, have been discussed. Finally, the…
We introduce and study a natural notion of probabilistic 1-Lipschitz maps. We prove that the space of all probabilistic 1-Lipschitz maps defined on a probabilistic metric space G is also a probabilistic metric space. Moreover, when G is a…
We obtain sharp approximation results for into nearisometries between Lp spaces and nearisometries into a Hilbert space. Our main theorem is the optimal approximation result for nearsurjective nearisometries between general Banach spaces.
In this paper, first we present a new useful way of formulating probabilistic normed spaces. Then by using this formulation and probabilistic normed space version of the Baire category theorem, we prove four important results of functional…
The aim of this paper is to review the state-of-the-art of recent research concerning the numerical index of Banach spaces, by presenting some of the results found in the last years and proposing a number of related open problems.