Related papers: Square roots of some classical operators
Recent work by several authors has revealed the existence of many unexpected classes of normal weighted composition operators. On the other hand, it is known that every normal operator is a complex symmetric operator. We therefore undertake…
We provide a brief survey of a certain algebra of operators on symmetric polynomials, and collect a number of previously known results in the field.
The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Pel\'{a}ez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for…
Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…
A description of the real, complete modules over the Clifford algebra of a Hilbert space, with the elements of the latter acting by skew-symmetric operators.
We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for Ces\`aro bounded operators of fractional order. The results obtained fairly generalize the corresponding ones for…
The main goal of this paper is to show that a (not necessarily densely defined or closed) symmetric operator $A$ acting on a real or complex Hilbert space is selfadjoint exactly when $I+A^2$ is a full range operator.
This paper presents some properties and applications of "transversal operators". Two transversal operators are presented: a "translation" operator T and a "dilation" operator D. Such operators are used in common analysis systems including…
Primary fields of the $q$-deformed Virasoro algebra are constructed. Commutation relations among the primary fields are studied. Adjoint actions of the deformed Virasoro current on the primary fields are represented by the shift operator…
We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the…
Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its arithmetic Tutte polynomial.…
In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the AN operators, see Definition 1.2. The class of AN…
We investigate $\rho$-orthogonality and its local symmetry in the space of bounded linear operators. A characterization of Hilbert space operators with symmetric numerical range is established in terms of $\rho$-orthogonality. Further, we…
For a Hilbert space H included in L^1_{loc} (R) of functions on $R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L^2(R) as well as our…
In this paper, we use the theory of fractional powers of linear operators to construct a general (analytic) representation theory for the square-root energy operator of relativistic quantum theory, which is valid for all values of the spin.…
We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of scattering theory, but are independent of any perturbation…
In this paper, we investigate weighted composition, Volterra and Integral operators on second derivative Hardy spaces. Some equivalent conditions for boundedness of the operators will be given using the boundedness on the Hardy spaces. Also…
The numerical range of a bounded, linear operator on a Hilbert space is a set in $\mathbb{C}$ that encodes important information about the operator. In this survey paper, we first consider numerical ranges of matrices and discuss several…
This note aims to present novel positive linear operators involving the Wright function. Furthermore, the present research established the moments of these newly defined operators and estimated the convergence rate using the classical…
Recently, we have shown how the interpretation of quantum mechanics due to Lande' can be used to derive from first principles generalized formulas for the operators and some eigenvectors for spin 1/2 Though we gave the operators for all the…