Related papers: The structure of normal Hausdorff operators on Leb…
The main goal of this work is to examine the structure of normal Hausdorff operators on $\mathbb{R}^n$. We show that normal Hausdorff operator in $L^2(\mathbb{R}^n)$ is unitary equivalent to the operator of multiplication by some…
A general concept of a Hausdorff-type operator that absorbs all types of operators bearing the name `` Hausdorff operator'' and many others is considered. The characteristic features of this concept are the consideration of kernels…
In this paper, we study commutator of generalized Hausdorff operator on function spaces. We mainly discuss the continuity criteria for such commutator operator when the symbol functions are either from central-$BMO$ or Lipschitz class of…
A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration…
The aim of this work is to derive a symbol calculus on $L^2(\mathbb{R})$ for one-dimensional Hausdorff operators in apparently the most general form.
The general notion of a Hausdorff-type operator with a kernel depending on an external variable is introduced and generalizations and analogs of classical results on the regularity of various summation methods are proved for the case of…
This paper explores a version of the classical Ces`aro integral operator for the Lebesgue space L2(0, 1) where we discuss its norm, adjoint, spectral properties, and invariant subspaces. An important tool will be semigroups of weighted…
In this paper, we present a complete spectral research of generalized Ces\`aro operators on Sobolev-Lebesgue sequence spaces. The main idea is to subordinate such operators to suitable $C_0$-semigroups on these sequence spaces. We introduce…
Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author…
The aim of this work is to derive a symbol calculus on $L^2(\mathbb{R}^n)$ for multidimensional Hausdorff operators. Two aspects of this activity result in two almost independent parts. While throughout the perturbation matrices are…
In this paper, we introduce and study a new class of bounded linear operators on complex Hilbert spaces, which we call 2-C-normal operators. This class is inspired by and closely related to the notion of 2-normal operators, with additional…
In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant.…
We consider a generalization of Hausdorff operators on Lebesgue spaces and under natural conditions prove that such an operator is not a Riesz operator provided it is non-zero. In particular, it cannot be represented as a sum of a…
We obtain in this short article the non-asymptotic estimations for the norm of (generalized) Cesaro-Hardy integral operators in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these…
Rhaly operators, as generalizations of the Ces\`aro operator, are studied from the standpoint of view of spectral theory and invariant subspaces, extending previous results by Rhaly and Leibowitz to a framework where generalized Ces\`aro…
We consider generalized Hausdorff operators with positive definite and permutable perturbation matrices on Lebesgue spaces and prove that such operators are not Riesz operators provided they are non-zero.
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…
For a finite, positive, Borel measure $\mu$ on $(0,1)$ we consider an infinite matrix $\Gamma_\mu$, related to the classical Hausdorff matrix defined by the same measure $\mu$, in the same algebraic way that the Hilbert matrix is related to…
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 consider shift operators, self-adjoint, unitary and normal operators on the standard module over a unital C*-algebra A. We define various generalized spectra in A of these operators, give description of such spectra of…