Advertisement

On C*-Algebras of Super Toeplitz Operators with Radial Symbols

  • M. Loaiza
  • A. S’anchez-Nungaray
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 210)

Abstract

We study Toeplitz operators with radial symbols acting on the Bergman space of the super unit disk. We prove that, generalizing the classical case, every super Toeplitz operator with radial symbol is diagonal. This fact implies that the algebra generated by all super Toeplitz operators with radial symbols is commutative.

Mathematics Subject Classification (2000)

Primary 47B35 Secondary 47L80 32A36 58A50 

Keywords

Toeplitz operators commutative C*-algebras Bergman spaces supermanifolds and graded manifolds 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    F.A. Berezin, Introduction to Superanalysis, Reidel, Dordrecht, 1987.zbMATHGoogle Scholar
  2. [2]
    D. Borthwick, S. Klimek, A. Lesniewski, M. Rinaldi, Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds, Commun. Math. Phys. 153 (1993), 49–76.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    S. Grudsky, A. Karapetyants, N. Vasilevski, Dynamics of properties of Toeplitz Operators with radial symbols, Integral Equations and Operator Theory 50 (2004), 217–253.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    S. Grudsky, A. Karapetyants, N. Vasilevski, Toeplitz operators on the unit ball inn with radial symbols, Journal of Operator Theory 49 (2003), 325–346.zbMATHMathSciNetGoogle Scholar
  5. [5]
    S. Grudsky, R. Quiroga, N. Vasilevski, Commutative C *-algebras of Toeplitz operators and quantization on the unit disk, Journal of Functional Analysis 234 (2006), 1–44.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman Spaces, Springer-Verlag, New York, 2000.zbMATHGoogle Scholar
  7. [7]
    M. Loaiza, H. Upmeier, Toeplitz C *-algebras on super Cartan domains, Revista Matemática Complutense, vol. 21 (2), 489–518.Google Scholar
  8. [8]
    E. Prieto-Zanabria, Phd Dessertation 2007, CINVESTAV, Mexico.Google Scholar
  9. [9]
    R. Quiroga-Barranco, N. Vasilevski, Commutative algebras of Toeplitz operators on Reinhardt domains, Integral Equations and Operator Theory 59, 67–98, 2007.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Quiroga-Barranco R., and Vasilevski N., Commutative C *-algebra of Toeplitz operators on the unit ball, I. Bargmann type transform and spectral representations of Toeplitz operators, Integral Equations and Operator Theory, 59 (3):379–419,2007.CrossRefMathSciNetGoogle Scholar
  11. [11]
    Quiroga-Barranco R., and Vasilevski N., Commutative C *-algebra of Toeplitz operators on the unit ball, II. Geometry of the level sets of symbols, Integral Equations and Operator Theory, 59(1):89–132, 2008.Google Scholar
  12. [12]
    A. Sánchez-Nungaray, Commutative Algebras of Toeplitz Operators on the Supersphere of dimension (2|2) Phd Dissertation 2009, CINVESTAV, Mexico.Google Scholar
  13. [13]
    K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2005.Google Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • M. Loaiza
    • 1
  • A. S’anchez-Nungaray
    • 1
  1. 1.Departamento de MatemáticasCINVESTAVMéxicoMexico

Personalised recommendations