English
Related papers

Related papers: Recent progress on truncated Toeplitz operators

200 papers

This is a survey paper. We discuss Toeplitz operators in K\"ahler geometry, with applications to geometric quantization, and review some recent developments.

Symplectic Geometry · Mathematics 2008-04-25 Tatyana Foth

Asymmetric dual truncated Toeplitz operators acting between the orthogonal complements of two (eventually different) model spaces are introduced and studied. They are shown to be equivalent after extension to paired operators on…

Functional Analysis · Mathematics 2020-01-01 M. Cristina Câmara , Kamila Kliś-Garlicka , Bartosz Łanucha , Marek Ptak

In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions.

Functional Analysis · Mathematics 2013-07-23 Jonathan M. Borwein , Liangjin Yao

We investigate truncated Toeplitz operators belonging to the Schatten ideals. We completely characterize such operators when they have an analytic symbol or belong to the ideal of Hilbert-Schmidt operators. We also study model spaces…

Complex Variables · Mathematics 2014-10-09 Patrick Lopatto , Richard Rochberg

In this paper the authors show how to use Riemann-Hilbert techniques to prove various results, some old, some new, in the theory of Toeplitz operators and orthogonal polynomials on the unit circle (OPUC's). There are four main results: the…

Functional Analysis · Mathematics 2007-05-23 Percy Deift , Jorgen Ostensson

We prove a spatial Isomorphism between two spaces of matrix valued truncated Toeplitz operators.

Functional Analysis · Mathematics 2020-03-12 Rewayat Khan

This paper considers paired operators in the context of the Lebesgue Hilbert space $L^2$ on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are…

Functional Analysis · Mathematics 2025-01-22 M. Cristina Câmara , Jonathan R. Partington

A major open problem in the Theory of Toeplitz operators on the analytic Bergman space over the unit disk is the characterization of the commutant of a given Toeplitz operator--that is, the set of all bounded Toeplitz operators that commute…

Functional Analysis · Mathematics 2025-03-19 Aissa Bouhali , Issam Louhichi , Abdel Rahman Yousef

We consider the class of positive bounded and semi-continuous functions defined on the two dimensional torus If f belongs to this class, then f will be considered as the symbol of a Toeplitz operator truncated on a triangle parametrised by…

Functional Analysis · Mathematics 2013-02-26 Jean-Marc Rinkel , Abdellatif Seghier

In this paper, we study matrix representations of truncated Toeplitz operators with respect to orthonormal bases which are invariant under a canonical conjugation map. In particular, we determine necessary and sufficient conditions for when…

Functional Analysis · Mathematics 2023-02-27 Ryan O'Loughlin

The paper pursues three objectives. Firstly, we provide an expanded version of spectral analysis of self-adjoint Toeplitz operators, initially built by M. Rosenblum in the 1960's. We offer some improvements to Rosenblum's approach: for…

Spectral Theory · Mathematics 2022-01-27 Alexander V. Sobolev , Dmitri Yafaev

Matrix valued asymmetric truncated Toeplitz operator are compression of multiplication operators acting between two model spaces. These are the generalization of matrix valued truncated Toeplitz operators. In this paper we use generalized…

Functional Analysis · Mathematics 2020-08-12 Rewayat Khan

Given a contraction A on a Hilbert space H, an operator T on H is said to be A-invariant if <Tx,x>=<TAx,Ax> for every x in H such that ||Ax||=||x||. In the special case in which both defect indices of A are equal to 1, we show that every…

Functional Analysis · Mathematics 2017-05-01 H. Bercovici , D. Timotin

We reconsider studies of Toeplitz operators on function spaces (the weighted Bergman space, the generalized derivative Hardy space) and the H-Toeplitz operators on the Bergman space. Past studies have considered the presence or absence of…

Functional Analysis · Mathematics 2024-09-20 Chafiq Benhida , George R. Exner , Ji Eun Lee , Jongrak Lee

We study Toeplitz operators with respect to a commuting $n$-tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a particular such tuple on a function space. The algebra of…

Functional Analysis · Mathematics 2022-07-08 Tirthankar Bhattacharyya , B. Krishna Das , Haripada Sau

Toeplitz operators are met in different fields of mathematics such as stochastic processes, signal theory, completeness problems, operator theory, etc. In applications, spectral and mapping properties are of particular interest. In this…

Complex Variables · Mathematics 2015-11-30 Andreas Hartmann , Mishko Mitkovski

We discuss resent developments in the problem of description of finite rank Toeplitz operators in different Bergman spaces and give some applications in analysis and mathematical physics

Functional Analysis · Mathematics 2009-04-02 Grigori Rozenblum

Our goal is to compare various results for Toeplitz $T$ and Hankel $H$ operators. We consider semibounded operators and find necessary and sufficient conditions for their quadratic forms to be closable. This property allows one to define…

Functional Analysis · Mathematics 2017-11-08 D. R. Yafaev

The trace approximation problem for Toeplitz matrices and its applications to stationary processes dates back to the classic book by Grenander and Szeg\"o, "Toeplitz forms and their applications". It has then been extensively studied in the…

Probability · Mathematics 2013-04-25 Mamikon S. Ginovyan , Artur A. Sahakyan , Murad S. Taqqu

In this paper, we study Toeplitz operators on the weighted harmonic Bergman spaces with nonnegative symbols, the weights we choose here are Muckenhoupt A_2 weights. Results obtained include characterizations of bounded Toeplitz operators,…

Functional Analysis · Mathematics 2018-11-14 Zipeng Wang , Xianfeng Zhao