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Quasi-Radial Quasi-Homogeneous Symbols and Commutative Banach Algebras of Toeplitz Operators

Integral Equations and Operator Theory volume 66, pages 141–152 (2010)Cite this article

Abstract

We present here a quite unexpected result: Apart from already known commutative C*-algebras generated by Toeplitz operators on the unit ball, there are many other Banach algebras generated by Toeplitz operators which are commutative on each weighted Bergman space. These last algebras are non conjugated via biholomorphisms of the unit ball, non of them is a C*-algebra, and for n = 1 all of them collapse to the algebra generated by Toeplitz operators with radial symbols.

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References

  1. Grudsky S., Karapetyants A., Vasilevski N.: Toeplitz operators on the unit ball in C n with radial symbols. J. Operator Theory 49, 325–346 (2003)

    MATH  MathSciNet  Google Scholar 

  2. Grudsky S., Quiroga-Barranco R., Vasilevski N.: Commutative C*-algebras of Toeplitz operators and quantization on the unit disk. J. Funct. Anal., 234(1), 1–44 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Louhichi I., Rao N.V.: On Toeplitz operators with quasihomogeneous symbols. Atch. Math., 851, 248–257 (2005)

    Article  Google Scholar 

  4. Louhichi I., Rao N.V.: Bicommutants of Toeplitz operators. Atch. Math. 91, 256–264 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Issam Louhichi, Elizabeth Strouse, Lova Zakariasy: Products of Toeplitz operators on the Bergman space. Integral Equations Operator Theory 54(4), 525–539 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Raul Quiroga-Barranco, Nikolai Vasilevski: Commutative C*-algebras of Toeplitz operators on the unit ball, I. Bargmann-type transforms and spectral representations of Toeplitz operators. Integral Equations Operator Theory 59(3), 379–419 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Raul Quiroga-Barranco, Nikolai Vasilevski: Commutative C*-algebras of Toeplitz operators on the unit ball, II. Geometry of the level sets of symbols. Integral Equations Operator Theory 59(1), 89–132 (2008)

    Google Scholar 

  8. Ze-Hua Zhou and Xing-Tang Dong. Algebraic properties of Toeplitz operators with radial symbols on the Bergman space of the unit ball. Integral Equations and Operator Theory (to appear), 18 p.

  9. Kehe Zhu. Spaces of Holomorphic Functions in the Unit Ball. Springer Verlag, 2005.

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Authors and Affiliations

  1. Departamento de Matemáticas, CINVESTAV, Apartado Postal 14-740, 07000, México, D.F., México

    Nikolai Vasilevski

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  1. Nikolai Vasilevski
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Correspondence to Nikolai Vasilevski.

Additional information

This work was partially supported by CONACYT Project 80503, México.

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Vasilevski, N. Quasi-Radial Quasi-Homogeneous Symbols and Commutative Banach Algebras of Toeplitz Operators. Integr. Equ. Oper. Theory 66, 141–152 (2010). https://doi.org/10.1007/s00020-009-1732-8

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  • DOI: https://doi.org/10.1007/s00020-009-1732-8

Mathematics Subject Classification (2010)

  • Primary 47B35
  • Secondary 47L80
  • 32A36

Keywords

  • Toeplitz operator
  • weighted Bergman space
  • commutative Banach algebra
  • quasi-radial quasi-homogeneous symbol