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Journal articles on the topic 'Toeplitz operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 March 2023

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1

Jurasik, Joanna, and Bartosz Łanucha. "Asymmetric truncated Toeplitz operators equal to the zero operator." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 70, no. 2 (December 24, 2016): 51. http://dx.doi.org/10.17951/a.2016.70.2.51.

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Asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These operators are natural generalizations of truncated Toeplitz operators. In this paper we describe symbols of asymmetric truncated Toeplitz operators equal to the zero operator.

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2

Murphy, G. J. "Toeplitz Operators." Irish Mathematical Society Bulletin 0022 (1989): 42–49. http://dx.doi.org/10.33232/bims.0022.42.49.

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3

Zhang, Bo, Yanyue Shi, and Yufeng Lu. "Algebraic Properties of Toeplitz Operators on the Polydisk." Abstract and Applied Analysis 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/962313.

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We discuss some algebraic properties of Toeplitz operators on the Bergman space of the polydiskDn. Firstly, we introduce Toeplitz operators with quasihomogeneous symbols and property (P). Secondly, we study commutativity of certain quasihomogeneous Toeplitz operators and commutators of diagonal Toeplitz operators. Thirdly, we discuss finite rank semicommutators and commutators of Toeplitz operators with quasihomogeneous symbols. Finally, we solve the finite rank product problem for Toeplitz operators on the polydisk.

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4

Agbor, Dieudonne. "Algebraic Properties of Toeplitz Operators on the Pluri-harmonic Fock Space." Journal of Mathematics Research 9, no. 6 (October 26, 2017): 67. http://dx.doi.org/10.5539/jmr.v9n6p67.

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We study some algebraic properties of Toeplitz operators with radial and quasi homogeneous symbols on the pluriharmonic Fock space over $\mathbb{C}^{n}$. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator, the zero-product problem for the product of two Toeplitz operators. Next we characterize the commutativity of Toeplitz operators with quasi homogeneous symbols and finally we study finite rank of the product of Toeplitz operators with quasi homogeneous symbols.

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5

Gu, Caixing, Dong-O. Kang, Eungil Ko, and Ji Eun Lee. "Binormal Toeplitz operators on the Hardy space." International Journal of Mathematics 30, no. 01 (January 2019): 1950001. http://dx.doi.org/10.1142/s0129167x19500010.

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We characterize binormal Toeplitz operators with analytic, or, coanalytic symbol functions. Furthermore, for a large class of nonanalytic, noncoanalytic Toeplitz operators which include Toeplitz operators with trigonometric or rational symbols, we prove that those Toeplitz operators are binormal if and only if they are normal. Some of the historically important examples of Toeplitz operators in the paper show that our problem is subtle and the above result is sharp.

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6

Yang, Jingyu, Liu Liu, and Yufeng Lu. "Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/578436.

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We study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-product problem for several Toeplitz operators with radial symbols. Next, we study the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols. Finally, we also investigate finite rank commutators and semicommutators of two Toeplitz operators with quasihomogeneous symbols.

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7

Nikpour, Mehdi. "On Some Algebraic and Operator-Theoretic Properties of λ-Toeplitz Operators." Journal of Operators 2015 (January 6, 2015): 1–8. http://dx.doi.org/10.1155/2015/172754.

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Based on a spectral problem raised by Barría and Halmos, a new class of Hardy-Hilbert space operators, containing the classical Toeplitz operators, is introduced, and some of their Toeplitz-like algebraic and operator-theoretic properties are studied and explored.

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8

Nakazi, Takahiko. "Absolute Values of Toeplitz Operators and Hankel Operators." Canadian Mathematical Bulletin 34, no. 2 (June 1, 1991): 249–53. http://dx.doi.org/10.4153/cmb-1991-040-1.

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AbstractNehari's theorem for norms of bounded Hankel operators is revisited. Using it, the absolute values of Toeplitz operators are studied. This gives a theorem of Widom and Devinatz for invertible Toeplitz operators.

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9

Liu, Lanzhe. "Weighted boundedness for Toeplitz type operator associated to general integral operators." Asian-European Journal of Mathematics 07, no. 02 (June 2014): 1450026. http://dx.doi.org/10.1142/s1793557114500260.

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In this paper, we establish the weighted sharp maximal function estimates for the Toeplitz type operators associated to some integral operators and the weighted Lipschitz and BMO functions. As an application, we obtain the boundedness of the Toeplitz type operators on weighted Lebesgue and Morrey spaces. The operator includes Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.

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10

Engliš, Miroslav. "Toeplitz operators and localization operators." Transactions of the American Mathematical Society 361, no. 02 (August 18, 2008): 1039–52. http://dx.doi.org/10.1090/s0002-9947-08-04547-9.

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11

Zheng, Dechao. "Toeplitz operators and Hankel operators." Integral Equations and Operator Theory 12, no. 2 (March 1989): 280–99. http://dx.doi.org/10.1007/bf01195117.

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12

Kang, Si Ho. "COMPACT TOEPLITZ OPERATORS." Honam Mathematical Journal 35, no. 3 (September 25, 2013): 343–50. http://dx.doi.org/10.5831/hmj.2013.35.3.343.

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13

Sarason, Donald. "Unbounded Toeplitz Operators." Integral Equations and Operator Theory 61, no. 2 (April 17, 2008): 281–98. http://dx.doi.org/10.1007/s00020-008-1588-3.

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14

Baranov, Anton, and Andrei Lishanskii. "Hypercyclic Toeplitz Operators." Results in Mathematics 70, no. 3-4 (January 19, 2016): 337–47. http://dx.doi.org/10.1007/s00025-016-0527-x.

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15

Xia, Jin, Xiaofeng Wang, and Guangfu Cao. "Toeplitz Operators on Dirichlet-Type Space of Unit Ball." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/927513.

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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.

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16

Camara, M. Cristina, and Jonathan Partington. "Asymmetric truncated Toeplitz operators and Toeplitz operators with matrix symbol." Journal of Operator Theory 77, no. 2 (March 24, 2017): 455–79. http://dx.doi.org/10.7900/jot.2016apr27.2108.

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17

Guan, Hongyan, Liu Liu, and Yufeng Lu. "Algebraic Properties of Quasihomogeneous and Separately Quasihomogeneous Toeplitz Operators on the Pluriharmonic Bergman Space." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/252037.

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We study some algebraic properties of Toeplitz operator with quasihomogeneous or separately quasihomogeneous symbol on the pluriharmonic Bergman space of the unit ball inℂn. We determine when the product of two Toeplitz operators with certain separately quasi-homogeneous symbols is a Toeplitz operator. Next, we discuss the zero-product problem for several Toeplitz operators, one of whose symbols is separately quasihomogeneous and the others are quasi-homogeneous functions, and show that the zero-product problem for two Toeplitz operators has only a trivial solution if one of the symbols is separately quasihomogeneous and the other is arbitrary. Finally, we also characterize the commutativity of certain quasihomogeneous or separately quasihomogeneous Toeplitz operators.

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18

Ding, Qian, Yong Chen, and Yufeng Lu. "Commuting Toeplitz and Hankel Operators on Harmonic Dirichlet Spaces." Journal of Function Spaces 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/9627109.

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On the harmonic Dirichlet space of the unit disk, the commutativity of Toeplitz and Hankel operators is studied. We obtain characterizations of commuting Toeplitz and Hankel operators and essentially commuting (semicommuting) Toeplitz and Hankel operators with general symbols.

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19

Guediri, Hocine. "Quasinormality and Numerical Ranges of Certain Classes of Dual Toeplitz Operators." Abstract and Applied Analysis 2010 (2010): 1–14. http://dx.doi.org/10.1155/2010/426319.

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The study of dual Toeplitz operators was elaborated by Stroethoff and Zheng (2002), where various corresponding algebraic and spectral properties were established. In this paper, we characterize numerical ranges of certain classes of dual Toeplitz operators. Moreover, we introduce the analog of Halmos' fifth classification problem for quasinormal dual Toeplitz operators. In particular, we show that there are no quasinormal dual Toeplitz operators with bounded analytic or coanalytic symbols which are not normal.

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20

Lin, HongZhao, and YuFeng Lu. "Toeplitz Operators on the Dirichlet Space of𝔹n." Abstract and Applied Analysis 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/958201.

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We study the algebraic properties of Toeplitz operators on the Dirichlet space of the unit ball𝔹n. We characterize pluriharmonic symbol for which the corresponding Toeplitz operator is normal or isometric. We also obtain descriptions of conjugate holomorphic symbols of commuting Toeplitz operators. Finally, the commuting problem of Toeplitz operators whose symbols are of the formzpz¯qϕ(|z|2)is studied.

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21

Basor, Estelle, Albrecht Böttcher, and Torsten Ehrhardt. "Harold Widom’s work in Toeplitz operators." Bulletin of the American Mathematical Society 59, no. 2 (January 7, 2022): 175–90. http://dx.doi.org/10.1090/bull/1758.

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This is a survey of Harold Widom’s work in Toeplitz operators, embracing his early results on the invertibility and spectral theory of Toeplitz operators, his investigations of the eigenvalue distribution of convolution operators, and his groundbreaking research into Toeplitz and Wiener–Hopf determinants.

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22

Pták, Vlastimil. "Factorization of Toeplitz and Hankel operators." Mathematica Bohemica 122, no. 2 (1997): 131–45. http://dx.doi.org/10.21136/mb.1997.125920.

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23

Altun, Muhammed. "Fine Spectra of Symmetric Toeplitz Operators." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/932785.

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The fine spectra of 2-banded and 3-banded infinite Toeplitz matrices were examined by several authors. The fine spectra ofn-banded triangular Toeplitz matrices and tridiagonal symmetric matrices were computed in the following papers: Altun, “On the fine spectra of triangular toeplitz operators” (2011) and Altun, “Fine spectra of tridiagonal symmetric matrices” (2011). Here, we generalize those results to the ()-banded symmetric Toeplitz matrix operators for arbitrary positive integer .

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24

Maji, Amit, Jaydeb Sarkar, and Srijan Sarkar. "Toeplitz and asymptotic Toeplitz operators onH2(Dn)." Bulletin des Sciences Mathématiques 146 (July 2018): 33–49. http://dx.doi.org/10.1016/j.bulsci.2018.03.005.

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25

Seddighi, K. "On Quasisimilarity for Toeplitz Operators." Canadian Mathematical Bulletin 28, no. 1 (March 1, 1985): 107–12. http://dx.doi.org/10.4153/cmb-1985-012-4.

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AbstractIn this article we give a sufficient condition for quasisimilar analytic Toeplitz operators to be unitarily equivalent. We also use a result of Deddens and Wong to give a sufficient condition for an operator intertwining two analytic Toeplitz operators to intertwine their inner parts too. Analytic Toeplitz operators with univalent symbols satisfying a suitable normalization that are quasisimilar are shown to have equal symbols.

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26

Lee, Jongrak. "Normal Toeplitz Operators on the Fock Spaces." Symmetry 12, no. 10 (September 29, 2020): 1615. http://dx.doi.org/10.3390/sym12101615.

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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).

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27

Abreu, Luís Daniel, and Nelson Faustino. "On Toeplitz operators and localization operators." Proceedings of the American Mathematical Society 143, no. 10 (June 16, 2015): 4317–23. http://dx.doi.org/10.1090/proc/12211.

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28

Kim, Sumin, and Jongrak Lee. "Normal Toeplitz Operators on the Bergman Space." Mathematics 8, no. 9 (September 1, 2020): 1463. http://dx.doi.org/10.3390/math8091463.

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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).

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29

Lin, Yan, and Mengmeng Zhang. "WeightedBMOEstimates for Toeplitz Operators on Weighted Lebesgue Spaces." Journal of Function Spaces 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/349535.

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The authors establish the weightedBMOestimates for a class of Toeplitz operators related to strongly singular Calderón-Zygmund operators on weighted Lebesgue spaces. Moreover, the corresponding result for the Toeplitz operators related to classical Calderón-Zygmund operators can be deduced.

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30

Park, Efton. "Toeplitz Algebras and Extensions of Irrational Rotation Algebras." Canadian Mathematical Bulletin 48, no. 4 (December 1, 2005): 607–13. http://dx.doi.org/10.4153/cmb-2005-056-2.

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AbstractFor a given irrational number θ, we define Toeplitz operators with symbols in the irrational rotation algebra , and we show that the C*-algebra generated by these Toeplitz operators is an extension of by the algebra of compact operators. We then use these extensions to explicitly exhibit generators of the group KK1(, ℂ). We also prove an index theorem for that generalizes the standard index theorem for Toeplitz operators on the circle.

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31

Jiang, Cao, Xing-Tang Dong, and Ze-Hua Zhou. "Commuting and Semi-commuting Monomial-type Toeplitz Operators on Some Weakly Pseudoconvex Domains." Canadian Mathematical Bulletin 62, no. 02 (January 9, 2019): 327–40. http://dx.doi.org/10.4153/cmb-2018-026-1.

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AbstractIn this paper, we completely characterize the finite rank commutator and semi-commutator of two monomial-type Toeplitz operators on the Bergman space of certain weakly pseudoconvex domains. Somewhat surprisingly, there are not only plenty of commuting monomial-type Toeplitz operators but also non-trivial semi-commuting monomial-type Toeplitz operators. Our results are new even for the unit ball.

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32

Murphy, Gerard J. "Inner Functions and Toeplitz Operators." Canadian Mathematical Bulletin 36, no. 3 (September 1, 1993): 324–31. http://dx.doi.org/10.4153/cmb-1993-045-9.

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AbstractWe give characterizations of Toeplitz operators on generalised H2 spaces and derive some properties of the corresponding Toeplitz algebras. The proofs depend essentially on having a "sufficient" supply of inner functions.

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33

Zhang, Bo, and Yufeng Lu. "Toeplitz Operators with Quasihomogeneous Symbols on the Bergman Space of the Unit Ball." Journal of Function Spaces and Applications 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/414201.

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We consider when the product of two Toeplitz operators with some quasihomogeneous symbols on the Bergman space of the unit ball equals a Toeplitz operator with quasihomogeneous symbols. We also characterize finite-rank semicommutators or commutators of two Toeplitz operators with quasihomogeneous symbols.

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34

Liu, Chaomei, and Yufeng Lu. "Product and Commutativity ofkth-Order Slant Toeplitz Operators." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/473916.

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The commutativity ofkth-order slant Toeplitz operators with harmonic polynomial symbols, analytic symbols, and coanalytic symbols is discussed. We show that, on the Lebesgue space and Bergman space, necessary and sufficient conditions for the commutativity ofkth-order slant Toeplitz operators are that their symbol functions are linearly dependent. Also, we study the product of twokth-order slant Toeplitz operators and give some necessary and sufficient conditions.

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35

Cichoń, Dariusz, and Harold S. Shapiro. "Toeplitz operators in Segal-Bargmann spaces of vector-valued functions vector-valued functions." MATHEMATICA SCANDINAVICA 93, no. 2 (December 1, 2003): 275. http://dx.doi.org/10.7146/math.scand.a-14424.

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We discuss new results concerning unbounded Toeplitz operators defined in Segal-Bargmann spaces of (vector-valued) functions, i.e. the space of all entire functions which are square summable with respect to the Gaussian measure in $\mathrm{C}^n$. The problem of finding adjoints of analytic Toeplitz operators is solved in some cases. Closedness of the range of analytic Toeplitz operators is studied. We indicate an example of an entire function inducing a Toeplitz operator, for which the space of polynomials is not a core though it is contained in its domain.

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36

Arora, Subhash Chander, and Jyoti Bhola. "Essentially slant Toeplitz operators." Banach Journal of Mathematical Analysis 3, no. 2 (2009): 1–8. http://dx.doi.org/10.15352/bjma/1261086703.

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37

Yafaev, D. R. "On semibounded Toeplitz operators." Journal of Operator Theory 77, no. 1 (January 31, 2017): 205–16. http://dx.doi.org/10.7900/jot.2016mar20.2095.

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38

Charles, Laurent. "Analytic Berezin–Toeplitz operators." Mathematische Zeitschrift 299, no. 1-2 (March 4, 2021): 1015–35. http://dx.doi.org/10.1007/s00209-021-02720-y.

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39

Cowen, Carl C. "Hyponormality of Toeplitz operators." Proceedings of the American Mathematical Society 103, no. 3 (March 1, 1988): 809. http://dx.doi.org/10.1090/s0002-9939-1988-0947663-4.

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40

Ma, Pan, and Dechao Zheng. "Compact truncated Toeplitz operators." Journal of Functional Analysis 270, no. 11 (June 2016): 4256–79. http://dx.doi.org/10.1016/j.jfa.2016.01.023.

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41

Murphy, G. J. "Toeplitz operators and algebras." Mathematische Zeitschrift 208, no. 1 (December 1991): 355–62. http://dx.doi.org/10.1007/bf02571532.

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42

Chu, Cheng. "Normal Truncated Toeplitz Operators." Complex Analysis and Operator Theory 12, no. 4 (October 29, 2017): 849–57. http://dx.doi.org/10.1007/s11785-017-0740-y.

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43

Curto, Raúl E., Paul S. Muhly, and Jingbo Xia. "Toeplitz operators on flows." Journal of Functional Analysis 93, no. 2 (October 1990): 391–450. http://dx.doi.org/10.1016/0022-1236(90)90133-6.

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44

NAKAZI, Takahiko. "Kernels of Toeplitz operators." Journal of the Mathematical Society of Japan 38, no. 4 (October 1986): 607–16. http://dx.doi.org/10.2969/jmsj/03840607.

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45

Hwang, In Sung, and An Hyun Kim. "Hyponormal trigonometric Toeplitz operators." Operators and Matrices, no. 3 (2013): 573–85. http://dx.doi.org/10.7153/oam-07-31.

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46

Gorkin, Pamela, and Dechao Zheng. "Essentially commuting Toeplitz operators." Pacific Journal of Mathematics 190, no. 1 (September 1, 1999): 87–109. http://dx.doi.org/10.2140/pjm.1999.190.87.

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47

Ding, Xuanhao, and Yuanqi Sang. "Dual truncated Toeplitz operators." Journal of Mathematical Analysis and Applications 461, no. 1 (May 2018): 929–46. http://dx.doi.org/10.1016/j.jmaa.2017.12.032.

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48

Louhichi, I., and N. V. Rao. "Bicommutants of Toeplitz operators." Archiv der Mathematik 91, no. 3 (August 6, 2008): 256–64. http://dx.doi.org/10.1007/s00013-008-2790-x.

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49

Hutník, Ondrej, and Mária Hutníková. "On Toeplitz localization operators." Archiv der Mathematik 97, no. 4 (October 2011): 333–44. http://dx.doi.org/10.1007/s00013-011-0307-5.

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50

Murphy, Gerard J. "Products of Toeplitz operators." Integral Equations and Operator Theory 27, no. 4 (December 1997): 439–45. http://dx.doi.org/10.1007/bf01192124.

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