S. Pott, E. Strouse, “Products of Toeplitz operators on the Bergman spaces $A_\alpha^2$”, Algebra i Analiz, 18:1 (2006), 144–161; St. Petersburg Math. J., 18:1 (2007), 105

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Algebra i Analiz, 2006, Volume 18, Issue 1, Pages 144–161 (Mi aa63)

This article is cited in 8 scientific papers (total in 8 papers)

Research Papers

Products of Toeplitz operators on the Bergman spaces

A_{α}^{2}

$A_\alpha^2$

S. Pott^a, E. Strouse^b

^a Department of Mathematics, University of Glasgow, Glasgow, UK
^b Departement de Mathematiques Pures, Université Bordeaux I, Talence, France

Full-text PDF (194 kB) Citations (8)

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Abstract: We give a sufficient and a necessary condition for the product of Toeplitz operators

T_{f}^{α} T_{¯ g}^{α}

$T^\alpha_fT^\alpha_{\bar g}$ , with

f

$f$ ,

g

$g$ analytic, to be bounded on the weighted Bergman space

$L^2_a(\mathbb D,(1-|z|^2)^\alpha dA)$ . We also show that the only compact product of weighted Toeplitz operators is the trivial one.

Keywords: weighted Bergman spaces, Toeplitz operators, reproducing kernel thesis.

Received: 03.10.2005

English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 1, Pages 105–118
DOI: https://doi.org/10.1090/S1061-0022-06-00945-9

Bibliographic databases:

Document Type: Article

MSC: 47B35, 32A36

Language: English

Citation: S. Pott, E. Strouse, “Products of Toeplitz operators on the Bergman spaces

$A_\alpha^2$ ”, Algebra i Analiz, 18:1 (2006), 144–161; St. Petersburg Math. J., 18:1 (2007), 105–118

Citation in format AMSBIB

\Bibitem{PotStr06}

\by S.~Pott, E.~Strouse

\paper Products of Toeplitz operators on the Bergman spaces~$A_\alpha^2$

\jour Algebra i Analiz

\yr 2006

\vol 18

\issue 1

\pages 144--161

\mathnet{http://mi.mathnet.ru/aa63}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2225216}

\zmath{https://zbmath.org/?q=an:1127.47028}

\transl

\jour St. Petersburg Math. J.

\yr 2007

\vol 18

\issue 1

\pages 105--118

\crossref{https://doi.org/10.1090/S1061-0022-06-00945-9}

Linking options:

https://www.mathnet.ru/eng/aa63

https://www.mathnet.ru/eng/aa/v18/i1/p144

This publication is cited in the following 8 articles:

Kehe Zhu, Fields Institute Communications, 87, Function Spaces, Theory and Applications, 2023, 331
Sehba B.F., “On the Weighted Estimate of the Bergman Projection”, Czech. Math. J., 68:2 (2018), 497–511
Rahm R., “the Essential Norm of Operators on l(2)-Valued Bergman-Type Function Spaces”, Complex Anal. Oper. Theory, 10:1 (2016), 69–96
Michalska M., Sobolewski P., “Bounded Toeplitz and Hankel Products on the Weighted Bergman Spaces of the Unit Ball”, J. Aust. Math. Soc., 99:2 (2015), 237–249
Mitkovski M., Wick B.D., “A Reproducing Kernel Thesis For Operators on Bergman-Type Function Spaces”, J. Funct. Anal., 267:7 (2014), 2028–2055
Kerr R., “Products of Toeplitz operators on a vector valued Bergman space”, Integral Equations Operator Theory, 66:3 (2010), 367–395
Lu Yu., Liu Ch., “Toeplitz and Hankel Products on Bergman Spaces of the Unit Ball”, Chin. Ann. Math. Ser. B, 30:3 (2009), 293–310
Grudsky S., Vasilevski N., “On the structure of the $C^*$ -algebra generated by Toeplitz operators with piece-wise continuous symbols”, Complex Anal. Oper. Theory, 2:4 (2008), 525–548

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	175
References:	81
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