Boletín de la Sociedad Matemática Mexicana

, Volume 22, Issue 1, pp 213–227 | Cite as

Toeplitz operators with quasi-separately radial symbols on the complex projective space

  • Miguel A. Morales-Ramos
  • Armando Sánchez-Nungaray
  • Josué Ramírez-Ortega
Original Article Area 3
  • 57 Downloads

Abstract

We study the Toeplitz operators with quasi-separately radial symbols over the complex projective space \({\mathbb {CP}}^n\). We describe such Toeplitz operators and we prove that each bounded operator is unitarily equivalent to a Toeplitz operator whose symbol is a finite sum of quasi-separately radial symbols.

Keywords

Toeplitz operators Quasi-separately radial symbols  Complex projective space 

Mathematics Subject Classification

47L80 47B35 

References

  1. 1.
    Brown, A., Halmos, P.R.: Algebraic properties of Toeplitz operators. J. Reine Angew. Math. 213, 89–102 (1963). (MR0160136)Google Scholar
  2. 2.
    Grudsky, S., Karapetyants, A., Vasilevski, N.: Toeplitz operators on the unit ball in \(\mathbb{C}^{n}\) with radial symbols. J. Oper. Theory 49, 325–346 (2003). (MR1991742)Google Scholar
  3. 3.
    Grudsky, S., Karapetyants, A., Vasilevski, N.: Dynamics of properties of Toeplitz operators with radial symbols. Integral Equ. Oper. Theory 20(2), 217–253 (2004). (Zbl 1120.47305, MR2099791)Google Scholar
  4. 4.
    Grudsky, S., Quiroga-Barranco, R., Vasilevski, N.: Commutative C-algebras of Toeplitz operators and quantization on the unit disk. J. Funct. Anal. 234(1), 1–144 (2006). (Zbl 1100.47023, MR2214138)Google Scholar
  5. 5.
    Grudsky, S., Vasilevski, N.: Bergman-Toeplitz operators: Radial component influence. Integral Equ. Oper. Theory 40(1), 16–33 (2001). (Zbl 0993.47023, MR1829512)Google Scholar
  6. 6.
    Helgason, S.: Differential geometry, Lie groups, and symmetric spaces. Pure and Applied Mathematics, vol. 80. Academic Press, Inc., New York (1978)Google Scholar
  7. 7.
    Kobayashi, S., Nomizu, K.: Foundations of differential geometry, vol. II. Reprint of the 1969 original. Wiley Classics Library. A Wiley-Interscience Publication, Wiley, New York (1996)Google Scholar
  8. 8.
    Griffiths, P., Harris, J.: Principles of algebraic geometry. Wiley, New York (1978)MATHGoogle Scholar
  9. 9.
    Louchi, I., Strouse, E., Zakariasy, L.: Products of Toeplitz operators on the Bergman space. Integral Equ. Oper. Theory 54, 525–539 (2006)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Quiroga-Barranco, R., Sánchez-Nungaray, A.: Commutative \(C^*\) algebras of Toeplitz operators on complex projective spaces. Integral Equ. Oper. Theory 71, 225–243 (2011). (MR2838143)Google Scholar
  11. 11.
    Quiroga-Barranco, R., Sánchez-Nungaray, A.: Toeplitz operators with quasi-radial quasi-homogeneous symbols and bundles of Lagrangian frames. J. Oper. Theory 71(1), 199–222 (2014)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Quiroga-Barranco, R., Vasilevski, N.: Commutative algebras of Toeplitz operators on the Reinhardt domains. Integral Equ. Oper. Theory 59, 67–98 (2007). (Zbl 1135.47057, MR2351275)Google Scholar
  13. 13.
    Quiroga-Barranco, R., Vasilevski, N.: Commutative \(C^{*}\)-algebras of Toeplitz operators on the unit ball, I. Bargmann type transforms and spectral representations of Toeplitz operators. Integral Equ. Oper. Theory 59(3), 379–419 (2007). (Zbl 1144.47024, MR2363015)Google Scholar
  14. 14.
    Vasilevski, N.: Toeplitz operators on the bergman spaces: inside-the-domain effects. Contemp. Math. 289, 79–146 (2001). (Zbl 1054.47512, MR1864540)Google Scholar
  15. 15.
    Vasilevski, N.: Quasi-radial quasi-homogeneous symbols and commutative Banach algebras of Toeplitz operators. Integral Equ. Oper. Theory 66(1), 141–152 (2010)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Sociedad Matemática Mexicana 2015

Authors and Affiliations

  • Miguel A. Morales-Ramos
    • 1
  • Armando Sánchez-Nungaray
    • 1
  • Josué Ramírez-Ortega
    • 1
  1. 1.Universidad VeracruzanaXalapaMexico

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