Related papers: The triangle of operators, topologies, bornologies
We introduce and study a family of integral operators in the Kantorovich sense for functions acting on locally compact topological groups. We obtain convergence results for the above operators with respect to the pointwise and uniform…
We study Toeplitz operators with separately radial and radial symbols on the weighted Bergman spaces on the unit ball. The unitary equivalence of such operators with multiplication operators on $\ell^2$ spaces was previously obtained by…
We survey and analyze different ways in which bornologies, coarse structures and uniformities on a group agree with the group operations.
We study some dynamical properties of composition operators defined on the space $\mathcal{P}(^m X)$ of $m$-homogeneous polynomials on a Banach space $X$ when $\mathcal{P}(^m X)$ is endowed with two different topologies: the one of uniform…
In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. Then by using…
A. Grothendieck proved at the end of his thesis that the space of slowly increasing functions and the space of rapidly decreasing distributions are bornological. Grothendieck's proof relies on the isomorphy of these spaces to a sequence…
We consider the class of positive bounded and semi-continuous functions defined on the two dimensional torus If f belongs to this class, then f will be considered as the symbol of a Toeplitz operator truncated on a triangle parametrised by…
Pisier's celebrated counterexample to Halmos's similarity-to-contractions problem was based on $2 \times 2$ upper triangular block operator matrices involving three classical operators: forward and backward shifts on the diagonal and Hankel…
In this paper, first we present a new useful way of formulating probabilistic normed spaces. Then by using this formulation and probabilistic normed space version of the Baire category theorem, we prove four important results of functional…
Our goal is to compare various results for Toeplitz $T$ and Hankel $H$ operators. We consider semibounded operators and find necessary and sufficient conditions for their quadratic forms to be closable. This property allows one to define…
This note is a complement to Pusz--Woronowicz's works on functional calculus for two positive forms from the viewpoint of operator theory. Based on an elementary, self-contained and purely Hilbert space operator explanation of their…
We study ergodicity of composition operators on rearrangement-invariant Banach function spaces. More precisely, we give a natural and easy-to-check condition on the symbol of the operator which entails mean ergodicity on a very large class…
This paper examines the equivalence between various set convergences, as studied in [7, 13, 22], induced by an arbitrary bornology $\mathcal{S}$ on a metric space $(X,d)$. Specifically, it focuses on the upper parts of the following set…
It is introduced an open class of linear operators on Banach and Hilbert spaces such that their non-wandering set is an infinite dimensional topologically mixing subspace. In certain cases, the non-wandering set coincides with the whole…
We discuss the range spaces of Toeplitz operators with co-analytic symbols where we focus on the boundary behavior of the functions in these spaces as well as a natural orthogonal decomposition of this range.
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of…
Convexity is an important notion in non linear optimization theory as well as in infinite dimensional functional analysis. As will be seen below, very simple and powerful tools will be derived from elementary duality arguments (which are…
The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over $\C$. In particular, we obtain rather strong necessary and sufficient…
In this paper, we introduce operator geodesically convex and operator convex-log functions and characterize some properties of them. Then apply these classes of functions to present several operator Azc\'{e}l and Minkowski type inequalities…
We propose a unifying approach to many approximation properties studied in the literature from the 1930s up to our days. To do so, we say that a Banach space E has the (I,J,{\tau})-approximation property if E-valued operators belonging to…