Related papers: Simple examples of non closable paranormal operato…
Pseudo-differential operators of type 1,1 are proved continuous from the Triebel--Lizorkin space $F^d_{p,1}$ to $L_p$ for $1\le p<\infty$, when of order d, and this is the largest possible domain among the Besov and Triebel--Lizorkin…
We introduce a new approximation technique into the context of complex dynamics that allows us to construct examples of transcendental entire functions with unbounded wandering domains. We provide examples of entire functions with an orbit…
In this article, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded closed symmetric operator.
Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded domains, focusing on those with integrable kernels having…
The demiclosedness principle is one of the key tools in nonlinear analysis and fixed point theory. In this note, this principle is extended and made more flexible by two mutually orthogonal affine subspaces. Versions for finitely many…
Motivated by structures that appear in deep neural networks, we investigate nonlinear composite models alternating proximity and affine operators defined on different spaces. We first show that a wide range of activation operators used in…
The theory of random sets is demonstrated to prove useful for the theory of random operators. A random operator is here defined by requiring the graph to be a random set. It is proved that the spectrum and the set of eigenvalues of random…
There has been a long-standing conjecture in Banach algebra that every amenable operator is similar to a normal operator. In this paper, we study the structure of amenable operators on Hilbert spaces. At first, we show that the conjecture…
We investigate the $n$th root problem for bounded operators on a Hilbert space within the class of conditionally positive definite (CPD) operators determined by the L\'evy--Khintchine formula. The class contains subnormal operators,…
In this paper we introduce and study a class of structured set-valued operators which we call union averaged nonexpansive. At each point in their domain, the value of such an operator can be expressed as a finite union of single-valued…
If $T$ is a semibounded self-adjoint operator in a Hilbert space $(H, \, (\cdot , \cdot))$ then the closure of the sesquilinear form $(T \cdot , \cdot)$ is a unique Hilbert space completion. In the non-semibounded case a closure is a…
Let $A$ be a densely defined closed operator in a complex Banach space $X.$ Conditions for left invertibility of operators of the form $\sum_{j=1}^\infty a_j (\alpha_j -A)^{-1}$ are given. Several examples are considered.
We present a counterexample showing that the graphical limit of maximally monotone operators might not be maximally monotone. We also characterize the directional differentiability of the resolvent of an operator $B$ in terms of existence…
The necessary and sufficient conditions are given for a sequence of complex numbers to be the periodic (or antiperiodic) spectrum of non-self-adjoint Dirac operator.
We consider sets of operations on a set A that are closed under permutation of variables, addition of dummy variables and composition. We describe these closed sets in terms of a Galois connection between operations and systems of pointed…
We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical…
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…
Partial operators can have void or unbounded spectra. Contrarily to what is written in Dunford-Schwarz, the reason is not in the fact they are unounded operators.
We present a brief introduction to the theory of operator limits of random matrices to non-experts. Several open problems and conjectures are given. Connections to statistics, integrable systems, orthogonal polynomials, and more, are…
We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. This operator is perturbed by a first order differential operator, the coefficients of which depend arbitrarily on a…