Related papers: The triangle of operators, topologies, bornologies
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…
A new approach to problems of the Uncertainty Principle in Harmonic Analysis, based on the use of Toeplitz operators, has brought progress to some of the classical problems in the area. The goal of this paper is to develop and systematize…
We review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a simple application of the triangle inequality. The operators…
We explore the canonical Grothendieck topology in some specific circumstances. First we use a description of the canonical topology to get a variant of Giraud's Theorem. Then we explore the canonical Grothendieck topology on the categories…
Ordered locally convex spaces is an important classes of spaces in the theory of ordered topological vector spaces just as locally convex spaces in the theory of topological vector spaces. Some special classes of ordered locally convex…
A standard technique in infinite dimensional holomorphy, which produced several useful results, uses the Borel transform to represent linear functionals on certain spaces of multilinear operators between Banach spaces as multilinear…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
An estimate for the norm of selfadjoint Toeplitz operators with a radial, bounded and integrable symbol is obtained. This emphasizes the fact that the norm of such operator is strictly less than the supremum norm of the symbol. Consequences…
The bornological convergence structures that have been studied recently as generalizations of Attouch-Wets convergence define pretopologies on hyperspaces. In this paper we characterize the topological reflections of these pretopologies and…
Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and…
Truncated Toeplitz operators are C--symmetric with respect to the canonical conjugation given on an appropriate model space. However, by considering only one conjugation one cannot characterize truncated Toeplitz operators. It will be…
This paper aims to study the dual of an extended locally convex space. In particular, we study the weak and weak* topologies as well as the topology of uniform convergence on bounded subsets of an extended locally convex space. As an…
In this note, we study the boundedness and compactness of integral operators $I_g$ and $T_g $ from analytic Morrey spaces to Bloch space. Furthermore, the norm and essential norm of those operators are given.
Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on…
We introduce a framework based on Rockafellar's perturbation theory to analyze and solve general nonsmooth convex minimization and monotone inclusion problems involving nonlinearly composed functions as well as linear compositions. Such…
We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.
We consider Toeplitz operators in the Fock space, under rather general conditions imposed on the symbols. It is proved that if the operator has finite rank and the symbol is a function then the operator and the symbol should be zero. The…
Let $T:Y\to X$ be a bounded linear operator between two normed spaces. We characterize compactness of $T$ in terms of differentiability of the Lipschitz functions defined on $X$ with values in another normed space $Z$. Furthermore, using a…