scholarly journals Normal Toeplitz Operators on the Fock Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1615
Author(s):  
Jongrak Lee
Keyword(s):  
Toeplitz Operator ◽  
Toeplitz Operators ◽  
Fock Spaces ◽  
Basic Properties

We characterize normal Toeplitz operator on the Fock spaces F2(C). First, we state basic properties for Toeplitz operator Tφ on F2(C). Next, we study the normal Toeplitz operator Tφ on F2(C) in terms of harmonic symbols φ. Finally, we characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on F2(C).

scholarly journals Normal Toeplitz Operators on the Bergman Space

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1463
Author(s):  
Sumin Kim ◽  
Jongrak Lee
Keyword(s):  
Toeplitz Operator ◽  
Bergman Space ◽  
Toeplitz Operators ◽  
Basic Properties

In this paper, we give a characterization of normality of Toeplitz operator Tφ on the Bergman space A2(D). First, we state basic properties for Toeplitz operator Tφ on A2(D). Next, we consider the normal Toeplitz operator Tφ on A2(D) in terms of harmonic symbols φ. Finally, we characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on A2(D).

scholarly journals Reducing Subspaces of the Dual Truncated Toeplitz Operator

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yinyin Hu ◽  
Jia Deng ◽  
Tao Yu ◽  
Liu Liu ◽  
Yufeng Lu
Keyword(s):  
Toeplitz Operator ◽  
Toeplitz Operators ◽  
Truncated Toeplitz Operator ◽  
Basic Properties ◽  
Reducing Subspaces

We define the dual truncated Toeplitz operators and give some basic properties of them. In particular, spectrum and reducing subspaces of some special dual truncated Toeplitz operator are characterized.

scholarly journals Toeplitz operators between large Fock spaces in several complex variables

2021 ◽  
Vol 7 (1) ◽  
pp. 1293-1306
Author(s):  
Ermin Wang ◽  
◽  
Jiajia Xu
Keyword(s):  
Toeplitz Operator ◽  
Toeplitz Operators ◽  
Borel Measure ◽  
Fock Space ◽  
Holomorphic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Weight Class ◽  
Fock Spaces ◽  
Positive Borel Measure

<abstract><p>Let $ \omega $ belong to the weight class $ \mathcal{W} $, the large Fock space $ \mathcal{F}_{\omega}^{p} $ consists of all holomorphic functions $ f $ on $ \mathbb{C}^{n} $ such that the function $ f(\cdot)\omega(\cdot)^{1/2} $ is in $ L^p(\mathbb{C}^{n}, dv) $. In this paper, given a positive Borel measure $ \mu $ on $ {\mathbb C}^n $, we characterize the boundedness and compactness of Toeplitz operator $ T_\mu $ between two large Fock spaces $ F^{p}_\omega $ and $ F^{q}_\omega $ for all possible $ 0 &lt; p, q &lt; \infty $.</p></abstract>

scholarly journals Hyponormality of Toeplitz operators with non-harmonic symbols on the Bergman spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sumin Kim ◽  
Jongrak Lee
Keyword(s):  
Toeplitz Operator ◽  
Bergman Space ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

AbstractIn this paper, we present some necessary and sufficient conditions for the hyponormality of Toeplitz operator $T_{\varphi }$ T φ on the Bergman space $A^{2}(\mathbb{D})$ A 2 ( D ) with non-harmonic symbols under certain assumptions.

scholarly journals Toeplitz Operators on Dirichlet-Type Space of Unit Ball

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Jin Xia ◽  
Xiaofeng Wang ◽  
Guangfu Cao
Keyword(s):  
Toeplitz Operator ◽  
Boundary Point ◽  
Toeplitz Operators ◽  
Radial Function ◽  
Type Space ◽  
Dirichlet Type ◽  
Algebraic Properties ◽  
Commuting Problem ◽  
Product Problem ◽  
Dirichlet Type Space

We construct a functionuinL2Bn, dVwhich is unbounded on any neighborhood of each boundary point ofBnsuch that Toeplitz operatorTuis a Schattenp-class0<p<∞operator on Dirichlet-type spaceDBn, dV. Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type spaceDBn, dV. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. We investigate the zero-product problem for several Toeplitz operators with radial symbols. Furthermore, the corresponding commuting problem of Toeplitz operators whose symbols are of the formξkuis studied, wherek ∈ Zn,ξ ∈ ∂Bn, anduis a radial function.

scholarly journals Hyponormal Toeplitz operators on H2(T) with polynomial symbols

1996 ◽  
Vol 144 ◽  
pp. 179-182 ◽  
Author(s):  
Dahai Yu
Keyword(s):  
Functional Equation ◽  
Hardy Space ◽  
Closed Form ◽  
Unit Circle ◽  
Toeplitz Operator ◽  
Explicit Expression ◽  
Complex Plane ◽  
Toeplitz Operators ◽  
Computing Process

Let T be the unit circle on the complex plane, H2(T) be the usual Hardy space on T, Tø be the Toeplitz operator with symbol Cowen showed that if f1 and f2 are functions in H such that is in Lø, then Tf is hyponormal if and only if for some constant c and some function g in H∞ with Using it, T. Nakazi and K. Takahashi showed that the symbol of hyponormal Toeplitz operator Tø satisfies and and they described the ø solving the functional equation above. Both of their conditions are hard to check, T. Nakazi and K. Takahashi remarked that even “the question about polynomials is still open” [2]. Kehe Zhu gave a computing process by way of Schur’s functions so that we can determine any given polynomial ø such that Tø is hyponormal [3]. Since no closed-form for the general Schur’s function is known, it is still valuable to find an explicit expression for the condition of a polynomial á such that Tø is hyponormal and depends only on the coefficients of ø, here we have one, it is elementary and relatively easy to check. We begin with the most general case and the following Lemma is essential.

scholarly journals Toeplitz Operators on the Weighted Pluriharmonic Bergman Space with Radial Symbols

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Zhi Ling Sun ◽  
Yu Feng Lu
Keyword(s):  
Toeplitz Operator ◽  
Bergman Space ◽  
Spectral Decomposition ◽  
Toeplitz Operators ◽  
Complete Information ◽  
Isometric Isomorphism

We construct an operatorRwhose restriction onto weighted pluriharmonic Bergman Spacebμ2(Bn)is an isometric isomorphism betweenbμ2(Bn)andl2#. Furthermore, using the operatorRwe prove that each Toeplitz operatorTawith radial symbols is unitary to the multication operatorγa,μI. Meanwhile, the Wick function of a Toeplitz operator with radial symbol gives complete information about the operator, providing its spectral decomposition.

scholarly journals The Detectable Subspace for the Friedrichs Model: Applications of Toeplitz Operators and the Riesz–Nevanlinna Factorisation Theorem

2020 ◽  
Vol 21 (10) ◽  
pp. 3141-3156
Author(s):  
S. Naboko ◽  
I. Wood
Keyword(s):  
Toeplitz Operator ◽  
Finite Rank ◽  
Toeplitz Operators ◽  
Model Operator ◽  
Hardy Classes ◽  
Finite Rank Perturbation ◽  
Boundary Measurements ◽  
Independent Variable ◽  
Friedrichs Model

Abstract We discuss how much information on a Friedrichs model operator (a finite rank perturbation of the operator of multiplication by the independent variable) can be detected from ‘measurements on the boundary’. The framework of boundary triples is used to introduce the generalised Titchmarsh–Weyl M-function and the detectable subspaces which are associated with the part of the operator which is ‘accessible from boundary measurements’. In this paper, we choose functions arising as parameters in the Friedrichs model in certain Hardy classes. This allows us to determine the detectable subspace by using the canonical Riesz–Nevanlinna factorisation of the symbol of a related Toeplitz operator.

Schatten-p class (0 < p ≤ ∞) Toeplitz operators on generalized Fock spaces

2015 ◽  
Vol 31 (4) ◽  
pp. 703-714 ◽  
Author(s):  
Lian Hua Xiao ◽  
Xiao Feng Wang ◽  
Jin Xia
Keyword(s):  
Toeplitz Operators ◽  
Fock Spaces
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