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Journal articles on the topic 'Bergman spaces. Toeplitz operators'

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Published: 4 June 2021
Last updated: 2 February 2022

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1

Faour, Nazih S. "Toeplitz operators on Bergman spaces." Rendiconti del Circolo Matematico di Palermo 35, no. 2 (June 1986): 221–32. http://dx.doi.org/10.1007/bf02844733.

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2

Chacón, Gerardo R. "Toeplitz Operators on Weighted Bergman Spaces." Journal of Function Spaces and Applications 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/753153.

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3

Engliš, Miroslav. "Some density theorems for Toeplitz operators on Bergman spaces." Czechoslovak Mathematical Journal 40, no. 3 (1990): 491–502. http://dx.doi.org/10.21136/cmj.1990.102402.

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4

Mannersalo, Paula. "Toeplitz operators on Bergman spaces of polygonal domains." Proceedings of the Edinburgh Mathematical Society 62, no. 4 (June 26, 2019): 1115–36. http://dx.doi.org/10.1017/s0013091519000105.

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AbstractWe study the boundedness of Toeplitz operators with locally integrable symbols on Bergman spaces Ap(Ω), 1 < p < ∞, where Ω ⊂ ℂ is a bounded simply connected domain with polygonal boundary. We give sufficient conditions for the boundedness of generalized Toeplitz operators in terms of ‘averages’ of symbol over certain Cartesian squares. We use the Whitney decomposition of Ω in the proof. We also give examples of bounded Toeplitz operators on Ap(Ω) in the case where polygon Ω has such a large corner that the Bergman projection is unbounded.
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5

STROETHOFF, KAREL. "Compact Toeplitz operators on Bergman spaces." Mathematical Proceedings of the Cambridge Philosophical Society 124, no. 1 (July 1998): 151–60. http://dx.doi.org/10.1017/s0305004197002375.

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Let Bn denote the open unit ball in Cn. We write V to denote Lebesgue volume measure on Bn normalized so that V(Bn)=1. Fix −1<γ<∞ and let Vγ denote the measure given by dVγ(z)=cγ (1−[mid ]z[mid ]2)γdV(z), for z∈Bn, where cγ=Γ(n+γ+1)/ (n!Γ(γ+1)); then Vγ(Bn)=1. The weighted Bergman space A2,γ(Bn) is the space of all analytic functions in L2(Bn, dVγ). This is a closed linear subspace of L2(Bn, dVγ). Let Pγ denote the orthogonal projection of L2(Bn, dVγ) onto A2,γ(Bn). For a function f∈L∞(Bn) the Toeplitz operator Tf is defined on A2,γ(Bn) by Tfh=Pγ(fh), for h∈A2,γ(Bn). It is clear that Tf is bounded on A2,γ(Bn) with ∥Tf∥[les ]∥f∥∞. In this paper we will consider the question for which f∈L∞(Bn) the operator Tf is compact on A2,γ(Bn). Although a complete answer has been given by the author and D. Zheng (see the next section), the condition for compactness is somewhat unnatural. In this article we will give a more natural description for compactness of Toeplitz operators with sufficiently nice symbols. We will describe compactness in terms of behaviour of the so-called Berezin transform of the symbol, which has been useful in characterizing compactness of Toeplitz operators with positive symbols (see [5, 9]). Before we can define this Berezin transform we need to introduce more notation.
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6

Choe, Boo Rim, Young Joo Lee, and Kyunguk Na. "Toeplitz operators on harmonic Bergman spaces." Nagoya Mathematical Journal 174 (2004): 165–86. http://dx.doi.org/10.1017/s0027763000008837.

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AbstractWe study Toeplitz operators on the harmonic Bergman spaces on bounded smooth domains. Two classes of symbols are considered; one is the class of positive symbols and the other is the class of uniformly continuous symbols. For positive symbols, boundedness, compactness, and membership in the Schatten classes are characterized. For uniformly continuous symbols, the essential spectra are described.
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7

Miao, Jie. "Toeplitz operators on harmonic Bergman spaces." Integral Equations and Operator Theory 27, no. 4 (December 1997): 426–38. http://dx.doi.org/10.1007/bf01192123.

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8

Chailuek, Kamthorn, and Brian C. Hall. "Toeplitz Operators on Generalized Bergman Spaces." Integral Equations and Operator Theory 66, no. 1 (January 2010): 53–77. http://dx.doi.org/10.1007/s00020-009-1734-6.

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9

Elias, Norma. "Toeplitz operators on weighted Bergman spaces." Integral Equations and Operator Theory 11, no. 3 (May 1988): 310–31. http://dx.doi.org/10.1007/bf01202076.

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10

Stroethoff, Karel. "Compact Toeplitz operators on weighted harmonic Bergman spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 64, no. 1 (February 1998): 136–48. http://dx.doi.org/10.1017/s144678870000135x.

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AbstractWe consider the Bergman spaces consisting of harmonic functions on the unit ball in Rn that are squareintegrable with respect to radial weights. We will describe compactness for certain classes of Toeplitz operators on these harmonic Bergman spaces.
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11

Lee, Young Joo. "Pluriharmonic Symbols of Commuting Toeplitz Type Operators on the Weighted Bergman Spaces." Canadian Mathematical Bulletin 41, no. 2 (June 1, 1998): 129–36. http://dx.doi.org/10.4153/cmb-1998-020-7.

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AbstractA class of Toeplitz type operators acting on the weighted Bergman spaces of the unit ball in the n-dimensional complex space is considered and two pluriharmonic symbols of commuting Toeplitz type operators are completely characterized.
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12

Kang, Si-Ho. "SOME TOEPLITZ OPERATORS ON WEIGHTED BERGMAN SPACES." Bulletin of the Korean Mathematical Society 48, no. 1 (January 31, 2011): 141–49. http://dx.doi.org/10.4134/bkms.2011.48.1.141.

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13

Lusky, Wolfgang. "Toeplitz operators on generalized Bergman-Hardy spaces." MATHEMATICA SCANDINAVICA 88, no. 1 (March 1, 2001): 96. http://dx.doi.org/10.7146/math.scand.a-14316.

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We study the Toeplitz operators $T_f: H_2 \to H_2$, for $f \in L_\infty$, on a class of spaces $H_2$ which in- cludes, among many other examples, the Hardy and Bergman spaces as well as the Fock space. We investigate the space $X$ of those elements $f \in L_\infty$ with $\lim_j \|T_f-T_{f_j}\|=0$ where $(f_j)$ is a sequence of vector-valued trigonometric polynomials whose coefficients are radial functions. For these $T_f$ we obtain explicit descriptions of their essential spectra. Moreover, we show that $f \in X$, whenever $T_f$ is compact, and characterize these functions in a simple and straightforward way. Finally, we determine those $f \in L_\infty$ where $T_f$ is a Hilbert-Schmidt operator.
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14

Nishio, Masaharu, Noriaki Suzuki, and Masahiro Yamada. "Compact Toeplitz operators on parabolic Bergman spaces." Hiroshima Mathematical Journal 38, no. 2 (July 2008): 177–92. http://dx.doi.org/10.32917/hmj/1220619455.

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15

Stroethoff, Karel, and De Chao Zheng. "Toeplitz and Hankel operators on Bergman spaces." Transactions of the American Mathematical Society 329, no. 2 (February 1, 1992): 773–94. http://dx.doi.org/10.1090/s0002-9947-1992-1112549-7.

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16

Wang, Zipeng, and Xianfeng Zhao. "Toeplitz operators on weighted harmonic Bergman spaces." Banach Journal of Mathematical Analysis 12, no. 4 (October 2018): 808–42. http://dx.doi.org/10.1215/17358787-2017-0049.

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17

Choi, Eun Sun. "Positive Toeplitz operators on pluriharmonic Bergman spaces." Journal of Mathematics of Kyoto University 47, no. 2 (2007): 247–67. http://dx.doi.org/10.1215/kjm/1250281046.

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18

Chacón, Gerardo R., and Humberto Rafeiro. "Toeplitz Operators on Variable Exponent Bergman Spaces." Mediterranean Journal of Mathematics 13, no. 5 (February 29, 2016): 3525–36. http://dx.doi.org/10.1007/s00009-016-0701-0.

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19

Le, Trieu, and Brian Simanek. "Hyponormal Toeplitz operators on weighted Bergman spaces." Integral Transforms and Special Functions 32, no. 5-8 (July 2, 2021): 560–67. http://dx.doi.org/10.1080/10652469.2020.1751153.

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20

Agbor, Dieudonne. "Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of C." International Journal of Mathematics and Mathematical Sciences 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/1417989.

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We study the compactness of some classes of bounded operators on the Bergman space with variable exponent. We show that via extrapolation, some results on boundedness of the Toeplitz operators with general L1 symbols and compactness of bounded operators on the Bergman spaces with constant exponents can readily be extended to the variable exponent setting. In particular, if S is a finite sum of finite products of Toeplitz operators with symbols from class BT, then S is compact if and only if the Berezin transform of S vanishes on the boundary of the unit disc.
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21

GUENTNER, ERIK, and NIGEL HIGSON. "A NOTE ON TOEPLITZ OPERATORS." International Journal of Mathematics 07, no. 04 (August 1996): 501–13. http://dx.doi.org/10.1142/s0129167x9600027x.

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We study Toeplitz operators on Bergman spaces using techniques from the analysis of Dirac-type operators on complete Riemannian manifolds, and prove an index theorem of Boutet de Monvel from this point of view. Our approach is similar to that of Baum and Douglas [2], but we replace boundary value theory for the Dolbeaut operator with much simpler estimates on complete manifolds.
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22

BAUER, WOLFRAM, and KENRO FURUTANI. "COMPACT OPERATORS AND THE PLURIHARMONIC BEREZIN TRANSFORM." International Journal of Mathematics 19, no. 06 (July 2008): 645–69. http://dx.doi.org/10.1142/s0129167x08004832.

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For a series of weighted Bergman spaces over bounded symmetric domains in ℂn, it has been shown by Axler and Zheng [1]; Englis [10] that the compactness of Toeplitz operators with bounded symbols can be characterized via the boundary behavior of its Berezin transform B a . In case of the pluriharmonic Bergman space, the pluriharmonic Berezin transform B ph fails to be one-to-one in general and even has non-compact operators in its kernel. From this point of view, perhaps surprisingly we show that via B ph the same characterization of compactness holds for Toeplitz operators on the pluriharmonic Fock space.
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23

Sadraoui, Houcine. "Hyponormality on general Bergman spaces." Filomat 33, no. 17 (2019): 5737–41. http://dx.doi.org/10.2298/fil1917737s.

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A bounded operator T on a Hilbert space is hyponormal if T*T-TT* is positive. We give a necessary condition for the hyponormality of Toeplitz operators on weighted Bergman spaces, for a certain class of radial weights, when the symbol is of the form f+g?, where both functions are analytic and bounded on the unit disk. We give a sufficient condition when f is a monomial.
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24

Lusky, Wolfgang, and Jari Taskinen. "Toeplitz operators on Bergman spaces and Hardy multipliers." Studia Mathematica 204, no. 2 (2011): 137–54. http://dx.doi.org/10.4064/sm204-2-3.

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25

Le, Trieu. "Toeplitz operators on radially weighted harmonic Bergman spaces." Journal of Mathematical Analysis and Applications 396, no. 1 (December 2012): 164–72. http://dx.doi.org/10.1016/j.jmaa.2012.06.006.

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26

Čučković, Željko, and Trieu Le. "Toeplitz operators on Bergman spaces of polyanalytic functions." Bulletin of the London Mathematical Society 44, no. 5 (April 6, 2012): 961–73. http://dx.doi.org/10.1112/blms/bds024.

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27

Perälä, Antti, Jari Taskinen, and Jani Virtanen. "Toeplitz operators with distributional symbols on Bergman spaces." Proceedings of the Edinburgh Mathematical Society 54, no. 2 (April 7, 2011): 505–14. http://dx.doi.org/10.1017/s001309151000026x.

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AbstractWe study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces $A^p(\mathbb{D})$, 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space $\smash{W_\nu^{-m,\infty}(\mathbb{D})}$ of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.
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28

Choi, Eun Sun. "Positive Toeplitz operators between the pluriharmonic Bergman spaces." Czechoslovak Mathematical Journal 58, no. 1 (March 2008): 93–111. http://dx.doi.org/10.1007/s10587-008-0007-x.

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29

Taskinen, Jari, and Jani Virtanen. "On compactness of Toeplitz operators in Bergman spaces." Functiones et Approximatio Commentarii Mathematici 59, no. 2 (December 2018): 305–18. http://dx.doi.org/10.7169/facm/1727.

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30

Hwang, In Sung, and Jongrak Lee. "Hyponormal Toeplitz operators on the weighted Bergman spaces." Mathematical Inequalities & Applications, no. 2 (2012): 323–30. http://dx.doi.org/10.7153/mia-15-26.

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31

Čučković, Željko, and Dashan Fan. "Commutants of Toeplitz operators on the ball and annulus." Glasgow Mathematical Journal 37, no. 3 (September 1995): 303–9. http://dx.doi.org/10.1017/s001708950003158x.

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In this paper we study commutants of Toeplitz operators with polynomial symbols acting on Bergman spaces of various domains. For a positive integer n, let V denote the Lebesgue volume measure on ℂn. If ω is a domain in ℂn, then the Bergman space is defined to be the set of all analytic functions from ω into ℂ such that
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32

MICHALSKA, MAŁGORZATA, and PAWEŁ SOBOLEWSKI. "BOUNDED TOEPLITZ AND HANKEL PRODUCTS ON THE WEIGHTED BERGMAN SPACES OF THE UNIT BALL." Journal of the Australian Mathematical Society 99, no. 2 (June 5, 2015): 237–49. http://dx.doi.org/10.1017/s1446788715000129.

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Let $A_{{\it\alpha}}^{p}$ be the weighted Bergman space of the unit ball in ${\mathcal{C}}^{n}$, $n\geq 2$. Recently, Miao studied products of two Toeplitz operators defined on $A_{{\it\alpha}}^{p}$. He proved a necessary condition and a sufficient condition for boundedness of such products in terms of the Berezin transform. We modify the Berezin transform and improve his sufficient condition for products of Toeplitz operators. We also investigate products of two Hankel operators defined on $A_{{\it\alpha}}^{p}$, and products of the Hankel operator and the Toeplitz operator. In particular, in both cases, we prove sufficient conditions for boundedness of the products.
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33

Lu, Yufeng. "Commuting of Toeplitz operators on the Bergman spaces of the bidisc." Bulletin of the Australian Mathematical Society 66, no. 2 (October 2002): 345–51. http://dx.doi.org/10.1017/s0004972700040181.

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34

PESSOA, LUÍS V. "TOEPLITZ OPERATORS AND THE ESSENTIAL BOUNDARY ON POLYANALYTIC FUNCTIONS." International Journal of Mathematics 24, no. 06 (June 2013): 1350042. http://dx.doi.org/10.1142/s0129167x13500420.

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Let j be a nonzero integer and let U be a bounded domain. We construct a Fredholm symbol calculus for the C*-algebra generated by the poly-Bergman projection and the operators of multiplication by continuous functions. We define the j-removal boundary in Hilbert spaces of polyanalytic functions and prove that the quotient poly-Toeplitz C*-algebra generated by cosets of poly-Toeplitz operators with continuous symbols is *-isomorphic to the C*-algebra of continuous functions over the j-essential boundary. Unlike the Bergman case, we also show that if j ≠ ±1 then the j-essential boundary coincides with the set of non-isolated points on the boundary.
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35

Lee, Jongrak, and Youho Lee. "HYPONORMALITY OF TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES." Honam Mathematical Journal 35, no. 2 (June 25, 2013): 311–17. http://dx.doi.org/10.5831/hmj.2013.35.2.311.

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36

NISHIO, Masaharu, Noriaki SUZUKI, and Masahiro YAMADA. "Toeplitz operators and Carleson measures on parabolic Bergman spaces." Hokkaido Mathematical Journal 36, no. 3 (August 2007): 563–83. http://dx.doi.org/10.14492/hokmj/1277472867.

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37

Taskinen, Jari, and Jani Virtanen. "On Fredholm properties of Toeplitz operators in Bergman spaces." Mathematical Methods in the Applied Sciences 43, no. 16 (February 8, 2020): 9405–15. http://dx.doi.org/10.1002/mma.6268.

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38

Choe, Boo Rim, and Kyesook Nam. "Berezin transform and Toeplitz operators on harmonic Bergman spaces." Journal of Functional Analysis 257, no. 10 (November 2009): 3135–66. http://dx.doi.org/10.1016/j.jfa.2009.08.006.

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39

Jiang, Chunlan, and Dechao Zheng. "Similarity of analytic Toeplitz operators on the Bergman spaces." Journal of Functional Analysis 258, no. 9 (May 2010): 2961–82. http://dx.doi.org/10.1016/j.jfa.2009.09.011.

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40

Li, Ran, and Yufeng Lu. "(m,λ)-Berezin Transform on the Weighted Bergman Spaces over the Polydisk." Journal of Function Spaces 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/6804235.

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We prove that every bounded linear operator on weighted Bergman space over the polydisk can be approximated by Toeplitz operators under some conditions. The main tool here is the so-called(m,λ)-Berezin transform. In particular, our results generalized the results of K. Nam and D. C. Zheng to the case of operators acting onAλ2(Dn).
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41

Fricain, Emmanuel, Javad Mashreghi, and Rishika Rupam. "Backward shift invariant subspaces in reproducing kernel Hilbert spaces." MATHEMATICA SCANDINAVICA 126, no. 1 (March 29, 2020): 142–60. http://dx.doi.org/10.7146/math.scand.a-119120.

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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.
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42

Nakazi, Takahiko, and Rikio Yoneda. "Compact Toeplitz operators with continuous symbols on weighted Bergman spaces." Glasgow Mathematical Journal 42, no. 1 (March 2000): 31–35. http://dx.doi.org/10.1017/s0017089500010053.

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Let L^2_a (D, d\sigma d\theta /2\pi ) be a complete weighted Bergman space on the open unit disc D, where d\sigma is a positive finite Borel measure on [0, 1). We show the following : when \phi is a continuous function on the closed unit disc \bar {D}, T_\phi is compact if and only if \phi = 0 on \partial D.1991 Mathematics Subject Classification 47B35, 47B07.
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43

Taskinen, Jari, and Jani Virtanen. "On generalized Toeplitz and little Hankel operators on Bergman spaces." Archiv der Mathematik 110, no. 2 (November 21, 2017): 155–66. http://dx.doi.org/10.1007/s00013-017-1124-2.

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44

LEE, Jongrak. "Hyponormality of block Toeplitz operators on the weighted Bergman spaces." Acta Mathematica Scientia 37, no. 6 (November 2017): 1695–704. http://dx.doi.org/10.1016/s0252-9602(17)30101-7.

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45

Pau, Jordi. "A remark on Schatten class Toeplitz operators on Bergman spaces." Proceedings of the American Mathematical Society 142, no. 8 (April 29, 2014): 2763–68. http://dx.doi.org/10.1090/s0002-9939-2014-12006-5.

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46

Hwang, In, Jongrak Lee, and Se Park. "Hyponormal Toeplitz operators with polynomial symbols on weighted Bergman spaces." Journal of Inequalities and Applications 2014, no. 1 (2014): 335. http://dx.doi.org/10.1186/1029-242x-2014-335.

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47

Le, Trieu. "On Toeplitz operators on Bergman spaces of the unit polydisk." Proceedings of the American Mathematical Society 138, no. 1 (January 1, 2010): 275–85. http://dx.doi.org/10.1090/s0002-9939-09-10060-6.

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48

Na, Kyunguk. "Positive Schatten(-Herz) Class Toeplitz Operators on Pluriharmonic Bergman Spaces." Integral Equations and Operator Theory 64, no. 3 (June 2, 2009): 409–28. http://dx.doi.org/10.1007/s00020-009-1688-8.

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49

Engliš, Miroslav. "Density of algebras generated by Toeplitz operators on Bergman spaces." Arkiv för Matematik 30, no. 1-2 (December 1992): 227–43. http://dx.doi.org/10.1007/bf02384872.

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50

Le, Trieu. "The commutants of certain Toeplitz operators on weighted Bergman spaces." Journal of Mathematical Analysis and Applications 348, no. 1 (December 2008): 1–11. http://dx.doi.org/10.1016/j.jmaa.2008.07.005.

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