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

This article is cited in 7 scientific papers (total in 7 papers)

Research Papers

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

S. Potta, E. Strouseb

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

Abstract: We give a sufficient and a necessary condition for the product of Toeplitz operators $T^\alpha_fT^\alpha_{\bar g}$, with $f$$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

Full text: PDF file (194 kB)
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English version:
St. Petersburg Mathematical Journal, 2007, 18:1, 105–118

Bibliographic databases:

MSC: 47B35, 32A36
Received: 03.10.2005
Language:

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://www.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}


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

    This publication is cited in the following articles:
    1. 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  crossref  mathscinet  zmath  isi  elib  scopus
    2. 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  crossref  mathscinet  zmath  isi  scopus
    3. Kerr R., “Products of Toeplitz operators on a vector valued Bergman space”, Integral Equations Operator Theory, 66:3 (2010), 367–395  crossref  mathscinet  zmath  isi  scopus
    4. Mitkovski M., Wick B.D., “A Reproducing Kernel Thesis For Operators on Bergman-Type Function Spaces”, J. Funct. Anal., 267:7 (2014), 2028–2055  crossref  mathscinet  zmath  isi  elib  scopus
    5. 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  crossref  mathscinet  zmath  isi  scopus
    6. Rahm R., “the Essential Norm of Operators on l(2)-Valued Bergman-Type Function Spaces”, Complex Anal. Oper. Theory, 10:1 (2016), 69–96  crossref  mathscinet  zmath  isi  scopus
    7. Sehba B.F., “On the Weighted Estimate of the Bergman Projection”, Czech. Math. J., 68:2 (2018), 497–511  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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