On a cell decomposition for Hankel matrices and rational functions.
On a class of Toeplitz + Hankel operators.
On a Hilbert-type operator with a symmetric homogeneous kernel of -order and applications.
On a similarity theory for rational Toeplitz operators.
On a weighted Toeplitz operator and its commutant.
On applicability of the projection method to two-dimensional Toeplitz operators with measurable symbol.
On approximation by Toeplitz operators
On Calderón-Toeplitz Operators.
On certain classes of variational inequalities and related iterative algorithms.
On finite sequences satisfying linear recursions.
On Hopf algebra deformation approach to renormalization.
On joint spectra of pairs of analytic Toeplitz operators
One computes the joint and essential joint spectra of a pair of multiplication operators with bounded analytic functions on the Hardy spaces of the unit ball in .
On products of some Toeplitz operators on polyanalytic Fock spaces
The purpose of this paper is to study the Sarason’s problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols and , we establish a necessary and sufficient condition for the boundedness of some Toeplitz products subjected to certain restriction on and . We also characterize this property in terms of the Berezin transform.
On Pták’s generalization of Hankel operators
In 1997 Pták defined generalized Hankel operators as follows: Given two contractions and , an operator is said to be a generalized Hankel operator if and satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of and . This approach, call it (P), contrasts with a previous one developed by Pták and Vrbová in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong but somewhat...
On S. Mazur's problems 8 and 88 from the Scottish Book
The paper discusses Problems 8 and 88 posed by Stanisław Mazur in the Scottish Book. It turns out that negative solutions to both problems are immediate consequences of the results of Peller [J. Operator Theory 7 (1982)]. We discuss here some quantitative aspects of Problems 8 and 88 and give answers to open problems discussed in a recent paper of Pełczyński and Sukochev in connection with Problem 88.
On self-commutators of Toeplitz operators with rational symbols
We prove that the self-commutator of a Toeplitz operator with unbounded analytic rational symbol has a dense domain in both the Bergman space and the Hardy space of the unit disc. This is a basic step towards establishing whether the self-commutator has a compact or trace-class extension.
On smooth extensions of odd dimensional spheres and multidimensional Helton and Howe formula.
On some problems connected with diagonal map in some spaces of analytic functions
For any holomorphic function on the unit polydisk we consider its restriction to the diagonal, i.e., the function in the unit disc defined by , and prove that the diagonal map maps the space of the polydisk onto the space of the unit disk.
On spectrality of the algebra of convolution dominated operators
If G is a discrete group, the algebra CD(G) of convolution dominated operators on l²(G) (see Definition 1 below) is canonically isomorphic to a twisted L¹-algebra . For amenable and rigidly symmetric G we use this to show that any element of this algebra is invertible in the algebra itself if and only if it is invertible as a bounded operator on l²(G), i.e. CD(G) is spectral in the algebra of all bounded operators. For G commutative, this result is known (see [1], [6]), for G noncommutative discrete...
On the approximation numbers of large Toeplitz matrices.