arXiv subjects

Kamila Kliś--Garlicka

Publications and source records attributed to Kamila Kliś--Garlicka.

4 recordsLinked to original sources

arXiv2020

Intertwining property for compressions of multiplication operators

Following Beurling's theorem the natural compressions of the multiplication operator in the classical $L^2$ space are compressions to model spaces and to their orthogonal complements. Two possibly different model spaces are considered hence asymmetric truncated Toeplitz and asymmetric dual truncated Toeplitz operators are investigated. The main purpose of the paper is to characterize operators which intertwine compressions of the unilateral shift.

math.FA↗

arXiv2019

Conjugations in $L^2$ and their invariants

Conjugations in space $L^2$ of the unit circle commuting with multiplication by $z$ or intertwining multiplications by $z$ and $\bar z$ are characterized. We also study their behaviour with respect to the Hardy space, subspaces invariant for the unilateral shift and model spaces.

math.FA↗

arXiv2019

Conjugations in $L^2(\mathcal{H})$

Conjugations commuting with $\mathbf{M}_z$ and intertwining $\mathbf{M}_z$ and $\mathbf{M}_{\bar z}$ in $L^2(\mathcal{H})$, where $\mathcal{H}$ is a Hilbert space, are characterized. We also investigate which of them leave invariant the whole Hardy space $H^2(\mathcal{H})$ or a model space $K_Θ=H^2(\mathcal{H})\ominusΘH^2(\mathcal{H})$, where $Θ$ is a pure operator valued inner function.

math.FA↗

arXiv2016

Characterizations of asymmetric truncated Toeplitz operators

The aim of this paper is to investigate asymmetric truncated Toeplitz operators with $L^2$ symbols between two different model spaces given by inner functions such that one divides the other. Characterizations of these operators are given in terms of rank two operators. A description of the class of symbols for which the corresponding asymmetric truncated Toeplitz operator is equal to the zero operator is also given.

math.FA↗