Positive Matrix Functions on the Bitorus with Prescribed Fourier Coefficients in a Band.
Positive Schatten class Toeplitz operators on the ball
On the harmonic Bergman space of the ball, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten class operator in terms of averaging functions and Berezin transforms.
Positive Schatten-Herz class Toeplitz operators on the ball.
Positive Toeplitz operators between the pluriharmonic Bergman spaces
We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space into another for in terms of certain Carleson and vanishing Carleson measures.
Preconditioners and Korovkin-type theorems for infinite-dimensional bounded linear operators via completely positive maps
The classical as well as noncommutative Korovkin-type theorems deal with the convergence of positive linear maps with respect to different modes of convergence, like norm or weak operator convergence etc. In this article, new versions of Korovkin-type theorems are proved using the notions of convergence induced by strong, weak and uniform eigenvalue clustering of matrix sequences with growing order. Such modes of convergence were originally considered for the special case of Toeplitz matrices and...
Probability against condition number and sampling of multivariate trigonometric random polynomials.
Problème spectral inverse et équation de Szegö cubique
Dans un exposé précédent [1], nous avons justifié l’introduction de l’équation de Szegö cubique comme cas modèle d’équation de type Schrödinger sans dispersion. Ce cas modèle s’est révélé être intéressant sous divers aspects [2]. Dans cet exposé, nous nous attacherons à montrer comment la complète intégrabilité de l’équation de Szegö cubique permet de résoudre un problème spectral inverse pour les opérateurs de Hankel.
Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space
We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators on the harmonic Bergman space is equal to a Toeplitz operator , then the product is also the Toeplitz operator , and hence commutes with . From this we give necessary and sufficient conditions for the product of two Toeplitz operators, one quasihomogeneous and the other monomial, to be a Toeplitz operator.
Products of Toeplitz operators and Hankel operators
We first determine when the sum of products of Hankel and Toeplitz operators is equal to zero; then we characterize when the product of a Toeplitz operator and a Hankel operator is a compact perturbation of a Hankel operator or a Toeplitz operator and when it is a finite rank perturbation of a Toeplitz operator.
Projections onto the spaces of Toeplitz operators
Projections onto the spaces of all Toeplitz operators on the N-torus and the unit sphere are constructed. The constructions are also extended to generalized Toeplitz operators and applied to show hyperreflexivity results.
Properties of the slant weighted Toeplitz operator.
Properties of two variables Toeplitz type operators
The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.
Quasinormal operators are hyperreflexive
We will prove the statement in the title. We also give a better estimate for the hyperreflexivity constant for an analytic Toeplitz operator.
Quasinormality and numerical ranges of certain classes of dual Toeplitz operators.
Rates of Convergence for the Approximation of Dual Shift-Invariant Systems in ... (...).
Reduced Cowen sets.
Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk
The reducing subspaces of Toeplitz operators on Dirichlet type spaces of the are described, which extends the results for the corresponding operators on Bergman spaces of the bidisk.
Reflexive Operator Algebras on Non-Commutative Hardy Spaces.
Remarks on extreme eigenvalues of Toeplitz matrices.
Reproducing kernels, Engliš algebras and some applications
We introduce the notion of Engliš algebras, defined in terms of reproducing kernels and Berezin symbols. Such algebras were apparently first investigated by Engliš (1995). Here we give some new results on Engliš C*-algebras on abstract reproducing kernel Hilbert spaces and some applications to various questions of operator theory. In particular, we give applications to Riccati operator equations, zero Toeplitz products, and the existence of invariant subspaces for some operators.