Related papers: On the Hilbert matrix operator: a brief survey
In this paper, we consider composition operators on weighted Hilbert spaces of analytic functions and observe that a formula for the essential norm, give a Hilbert-Schmidt characterization and characterize the membership in Schatten-class…
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…
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.
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.
In this paper the spectrum of composition operators on the space of real analytic functions is investigated. In some cases it is completely determined while in some other cases it is only estimated.
In the setting of modern mathematical logic and model theory, classification theory has been one of the landmark achievements of the field. Likewise, the classification of UHF-algebras and AF-algebras were substantial contributions to the…
The aim of this article is to present a brief overview of spectral perturbation theory for matrices, bounded linear operators and holomorphic operator-valued functions. We focus on bounds for perturbed eigenvalues, eigenvectors and…
In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.
In this note we investigate the operators associated with frame sequences in a Hilbert space $H$, i.e., the synthesis operator $T:\ell ^{2}(\mathbb{N}) \to H$, the analysis operator $T^{\ast}:H\to $ $% \ell ^{2}(\mathbb{N}) $ and the…
This is a brief survey which reviews some traditional themes in harmonic analysis and some more recent areas of activity, connected to "analysis on fractals" in particular.
We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on…
This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
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…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
Paul Halmos' work in dilation theory began with a question and its answer: Which operators on a Hilbert space can be extended to normal operators on a larger Hilbert space? The answer is interesting and subtle. The idea of representing…