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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…
Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces, random normed modules and random locally convex modules.…
This paper studies the large time existence for the motion of closed hypersurfaces in a radially symmetric potential. In physical, this surface can be considered as an electrically charged membrane with a constant charge per area in a…
This thesis addresses Pour-El and Richards' fourth question from their book "Computability in analysis and physics", concerning the relation between higher order recursion theory and computability in analysis. Among other things it is shown…
This is a survey of results on the classification of Banach spaces as metric spaces. It is based on a series of lectures I gave at the Functional Analysis Seminar in 1984-1985, and it appeared in the 1984-1985 issue of the Longhorn Notes. I…
The new class of Banach spaces, so-called asymptotic $l_p$ spaces, is introduced and it is shown that every Banach space with bounded distortions contains a subspace from this class. The proof is based on an investigation of certain…
It is well known that the description of topological and geometric properties of bisectors in normed spaces is a non-trivial subject. In this paper we introduce the concept of bounded representation of bisectors in finite dimensional real…
Results of a previous paper [Commun. Contemp. Math., 09 (2007) 217-251] on the existence of solutions to a nonlinear evolution equation in an abstract Lebesgue space, arising from kinetic theory, are re-obtained in the more general setting…
In this working note we study the one-sided positive Banach-Mazur distance between some pairs of $C(K)$ Banach spaces. Building on methods developed in [4], we solve, in particular, one of the problems posed in [2].
Let $E$ be a Banach space, and $\mathcal B(E)$ the algebra of all bounded linear operators on $E$. The question of amenability of $\mathcal B(E)$ goes back to Johnson's seminal memoir \cite{johnson} from 1972. We present the first general…
We modify the very well known theory of normed spaces $(E, \norm)$ within functional analysis by considering a sequence $(\norm_n : n\in\N)$ of norms, where $\norm_n$ is defined on the product space $E^n$ for each $n\in\N$. Our theory is…
It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present…
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…
In 2022, Hatori gave a sufficient condition for complex Banach spaces to have the complex Mazur--Ulam property. In this paper, we introduce a class of complex Banach spaces $B$ that do not satisfy the condition but enjoy the property that…
The Bayesian perspective on inverse problems has attracted much mathematical attention in recent years. Particular attention has been paid to Bayesian inverse problems (BIPs) in which the parameter to be inferred lies in an…
The standard theory of Banach spaces is built upon the notions of vector space, triangle inequality and Cauchy completeness. Here we propose a `hyperbolic' variant of this `elliptic' framework where general linear combinations are replaced…
The mixed area of a Reuleaux polygon and its symmetric with respect to the origin is expressed in terms of the mixed area of two explicit polygons. This gives a geometric explanation of a classical proof due to Chakerian. Mixed areas and…
The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder basis or an uncountable unconditional basis, easier and more transparent. The…
It is shown that two Banach spaces are linearly isometric if and only if the Gromov--Hausdorff distance between them is finite, in particular, zero. The proof is compilative and relies on results obtained by many researchers on the…
During the 1970s Br\'ezis and Browder presented a now classical characterization of maximal monotonicity of monotone linear relations in reflexive spaces. In this paper, we extend and refine their result to a general Banach space.