Related papers: The method of the weakly conjugate operator: Exten…
We introduce the notion of weakly associative algebra and its relations with the notion of nonassociative Poisson algebras.
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.
The weak convergence of orthogonal polynomials is given under conditions on the asymptotic behaviour of the coefficients in the three-term recurrence relation. The results generalize known results and are applied to several systems of…
We give some characterizations of disjointly weakly compact sets in Banach lattices, namely, those sets in whose solid hulls every disjoint sequence converges weakly to zero. As an application, we prove that a bounded linear operator from a…
Recently, many systems for graph analysis have been developed to address the growing needs of both industry and academia to study complex graphs. Insight into the practical uses of graph analysis will allow future developments of such…
In this paper we study Eulerian extensions with edge constraints and use the probabilistic method to establish sufficient conditions for a given connected graph to be a subgraph of a Eulerian graph containing $m$ edges, for a given number…
Higher-rank graph generalisations of the Popescu-Poisson transform are constructed, allowing us to develop a dilation theory for higher rank operator tuples. These dilations are joint dilations of the families of operators satisfying…
We investigate inexact proximity operators for weakly convex functions. To this aim, we derive sum rules for proximal {\epsilon}-subdifferentials, by incorporating the moduli of weak convexity of the functions into the respective formulas.…
Here we introduce connectivity operators, namely, diffusion operators, general Laplacian operators, and general adjacency operators for hypergraphs. These operators are generalisations of some conventional notions of apparently different…
We explore the relation of weak conjugacy in the group of homeomorphisms isotopic to the identity, for surfaces.
The aim of this paper is to introduce new forms of the weak and Omori-Yau maximum principles for linear operators, notably for trace type operators, and show their usefulness, for instance, in the context of PDE's and in the theory of…
In this article we introduce the {\it cylindrical construction} for graphs and investigate its basic properties. We state a main result claiming a weak tensor-like duality for this construction. Details of our motivations and applications…
We prove mixed weak estimates of Sawyer type for fractional operators. More precisely, let $\mathcal{T}$ be either the maximal fractional function $M_\gamma$ or the fractional integral operator $I_\gamma$, $0<\gamma<n$, $1\leq p<n/\gamma$…
We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures.…
In the symbol space for differential operators, we discuss a scalar type for change of local coordinates, using vector valued distributions. In particular, we discuss P-convexity for hypoelliptic operators.
We study different geometric properties on infinite graphs, related to the weak-type boundedness of the Hardy-Littlewood maximal averaging operator. In particular, we analyze the connections between the doubling condition, having finite…
Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear…
In this paper, we extend the concept of kings and serfs in tournaments to that of weak kings and weak serfs in oriented graphs. We obtain various results on the existence of weak kings(weak serfs) in oriented graphs, and show the existence…
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…
Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.