Related papers: Convergence theorems for graph sequences
Metric graphs are special types of metric spaces used to model and represent simple, ubiquitous, geometric relations in data such as biological networks, social networks, and road networks. We are interested in giving a qualitative…
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…
We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of piecewise-smooth maps of the interval where…
In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…
In \cite{Elek} we proved that the limit of a weakly convergent sequence of finite graphs can be viewed as a graphing or a continuous field of infinite graphs. Thus one can associate a type $II_1$-von Neumann algebra to such graph sequences.…
It is an open problem whether an infinite-dimensional amenable Banach algebra exists whose underlying Banach space is reflexive. We give sufficient conditions for a reflexive, amenable Banach algebra to be finite-dimensional (and thus a…
While numerous extensions of Banach's fixed point theorem typically offer only sufficient conditions for the existence and uniqueness of a fixed point and the convergence of iterative sequences, this study introduces a generalization…
We prove an implicit function theorem for C^k-maps from arbitrary topological vector spaces over valued fields to Banach spaces (for k at least 2). As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of…
This paper studies sequences of graphs satisfying the finite-time consensus property (i.e., iterating through such a finite sequence is equivalent to performing global or exact averaging) and their use in Gradient Tracking. We provide an…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…
A Banach space $X$ is said to have property (K) if every $w^*$-convergent sequence in $X^*$ admits a convex block subsequence which converges with respect to the Mackey topology. We study the connection of this property with strongly weakly…
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…
A theorem proved by Hrushovski for graphs and extended by Solecki and Vershik (independently from each other) to metric spaces leads to a stronger version of ultrahomogeneity of the infinite random graph $R$, the universal Urysohn metric…
This paper studies boundedness and closedness of linear relations, which include both single-valued and multi-valued linear operators. A new (single-valued) linear operator induced by a linear relation is introduced, and its relationships…
In this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a Banach space. We also study a Schauder fixed point property for a semitopological semigroup of…
For every filter $\mathcal F$ on $\mathbb N$, we introduce and study corresponding uniform $\mathcal F$-boundedness principles for locally convex topological vector spaces. These principles generalise the classical uniform boundedness…
We review and analyse techniques from the literature for extending a normed algebra, A to a normed algebra, B, so that B has interesting or desirable properties which A may lack. For example, B might include roots of monic polynomials over…
We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend…
We introduce a class of Banach algebras of generalized matrices and study the existence of approximate units, ideal structure, and derivations of them.