scholarly journals Bounded symbols and Reproducing Kernel Thesis for truncated Toeplitz operators

2010 ◽  
Vol 259 (10) ◽  
pp. 2673-2701 ◽  
Author(s):  
Anton Baranov ◽  
Isabelle Chalendar ◽  
Emmanuel Fricain ◽  
Javad Mashreghi ◽  
Dan Timotin
Keyword(s):  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Reproducing Kernel Thesis

scholarly journals The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

2021 ◽  
Author(s):  
Cezhong Tong ◽  
Junfeng Li ◽  
Hicham Arroussi
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Kernel Estimates ◽  
Berezin Transforms

AbstractIn this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.

scholarly journals Backward shift invariant subspaces in reproducing kernel Hilbert spaces

2020 ◽  
Vol 126 (1) ◽  
pp. 142-160
Author(s):  
Emmanuel Fricain ◽  
Javad Mashreghi ◽  
Rishika Rupam
Keyword(s):  
Hilbert Spaces ◽  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Bergman Spaces ◽  
Invariant Subspaces ◽  
Extreme Case ◽  
Reproducing Kernel Hilbert Spaces ◽  
Backward Shift ◽  
Kernel Hilbert Spaces ◽  
New Applications

In this note, we describe the backward shift invariant subspaces for an abstract class of reproducing kernel Hilbert spaces. Our main result is inspired by a result of Sarason concerning de Branges-Rovnyak spaces (the non-extreme case). Furthermore, we give new applications in the context of the range space of co-analytic Toeplitz operators and sub-Bergman spaces.

scholarly journals Toeplitz Operators on the Symmetrized Bidisc

2020 ◽  
Author(s):  
Tirthankar Bhattacharyya ◽  
B Krishna Das ◽  
Haripada Sau
Keyword(s):  
Hilbert Space ◽  
Hardy Space ◽  
Unit Disc ◽  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Multiplication Operators ◽  
Algebraic Characterization ◽  
Hilbert Modules ◽  
Symmetrized Bidisc

Abstract The symmetrized bidisc has been a rich field of holomorphic function theory and operator theory. A certain well-known reproducing kernel Hilbert space of holomorphic functions on the symmetrized bidisc resembles the Hardy space of the unit disc in several aspects. This space is known as the Hardy space of the symmetrized bidisc. We introduce the study of those operators on the Hardy space of the symmetrized bidisc that are analogous to Toeplitz operators on the Hardy space of the unit disc. More explicitly, we first study multiplication operators on a bigger space (an $L^2$-space) and then study compressions of these multiplication operators to the Hardy space of the symmetrized bidisc and prove the following major results. (1) Theorem I analyzes the Hardy space of the symmetrized bidisc, not just as a Hilbert space, but as a Hilbert module over the polynomial ring and finds three isomorphic copies of it as $\mathbb D^2$-contractive Hilbert modules. (2) Theorem II provides an algebraic, Brown and Halmos-type characterization of Toeplitz operators. (3) Theorem III gives several characterizations of an analytic Toeplitz operator. (4) Theorem IV characterizes asymptotic Toeplitz operators. (5) Theorem V is a commutant lifting theorem. (6) Theorem VI yields an algebraic characterization of dual Toeplitz operators. Every section from Section 2 to Section 7 contains a theorem each, the main result of that section.

scholarly journals Carleson potentials and the reproducing kernel thesis for embedding theorems

2007 ◽  
Vol 51 (4) ◽  
pp. 1249-1263 ◽  
Author(s):  
Stefanie Petermichl ◽  
Sergei Treil ◽  
Brett D. Wick
Keyword(s):  
Reproducing Kernel ◽  
Embedding Theorems ◽  
Reproducing Kernel Thesis
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