Related papers: Matrix dilation and Hausdorff operators on modulat…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
We prove sharp estimates for the dilation operator $f(x)\longmapsto f(\lambda x)$, when acting on Wiener amalgam spaces $W(L^p,L^q)$. Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations…
In this paper it is investigated how to find a matrix representation of operators on a Hilbert space with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs).…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
We give necessary and sufficient conditions for inhomogeneous Calder\'on-Zgymund operators to be bounded on the local hardy spaces $h^p(\mathbb{R}^n)$. We then give applications to local and truncated Riesz transforms, as well as…
The present work aims at obtaining estimates for transformation operators for one-dimensional perturbed radial Schr\"odinger operators. It provides more details and suitable extensions to already existing results, that are needed in other…
The aim of this paper is to characterize the nonnegative functions $\varphi$ defined on $(0,\infty)$ for which the Hausdorff operator $$\mathscr H_\varphi f(z)= \int_0^\infty f\left(\frac{z}{t}\right)\frac{\varphi(t)}{t}dt$$ is bounded on…
For a given bounded positive (semidefinite) linear operator $A$ on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$, we consider the semi-Hilbertian space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle_A…
Inspired by a recent work about distribution frames, the definition of multiplier operator is extended in the rigged Hilbert spaces setting and a study of its main properties is carried on. In particular, conditions for the density of…
We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.
Using the matrix representation of Fourier integral operators with respect to a Gabor frame, we study their compactness on weighted modulation spaces. As a consequence, we recover and improve some compactness results for pseudodifferential…
We study band-dominated operators on (subspaces of) $L_p$-spaces over metric measure spaces of bounded geometry satisfying an additional property. We single out core assumptions to obtain, in an abstract setting, definitions of limit…
In this paper, a sufficient condition for the existence of hyperinvariant subspace of compact perturbations of multiplication operators on some Banach spaces is presented. An interpretation of this result for compact perturbations of normal…
An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V from H to K such that C=V^*TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp…
This paper is devoted to studying the boundedness of multilinear operartors and their commutators on generalized weighted Morrey spaces, which includes multilinear fractional maximal operator and multilinear fractional integral operator.…
In this paper, we investigate the arithmetic Bohr radius of bounded linear operators between arbitrary complex Banach spaces. We establish the close connection between the classical Bohr radius and the arithmetic Bohr radius of bounded…
In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be…
This paper is devoted to studying some mixed radial-angular integrabilities for various types of Hausdorff operators and commutators
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
We completely characterize the Crawford number attainment set and the numerical radius attainment set of a bounded linear operator on a Hilbert space. We study the intersection properties of the corresponding attainment sets of numerical…