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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brown, A., Halmos, P.R.: Algebraic properties of Toeplitz operators. J. Reine Angew. Math. 213, 89–102 (1963). (MR0160136)
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)
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)
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)
Grudsky, S., Vasilevski, N.: Bergman-Toeplitz operators: Radial component influence. Integral Equ. Oper. Theory 40(1), 16–33 (2001). (Zbl 0993.47023, MR1829512)
Helgason, S.: Differential geometry, Lie groups, and symmetric spaces. Pure and Applied Mathematics, vol. 80. Academic Press, Inc., New York (1978)
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)
Griffiths, P., Harris, J.: Principles of algebraic geometry. Wiley, New York (1978)
Louchi, I., Strouse, E., Zakariasy, L.: Products of Toeplitz operators on the Bergman space. Integral Equ. Oper. Theory 54, 525–539 (2006)
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)
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)
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)
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)
Vasilevski, N.: Toeplitz operators on the bergman spaces: inside-the-domain effects. Contemp. Math. 289, 79–146 (2001). (Zbl 1054.47512, MR1864540)
Vasilevski, N.: Quasi-radial quasi-homogeneous symbols and commutative Banach algebras of Toeplitz operators. Integral Equ. Oper. Theory 66(1), 141–152 (2010)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was partially supported by CONACYT Project 236109.
Rights and permissions
About this article
Cite this article
Morales-Ramos, M.A., Sánchez-Nungaray, A. & Ramírez-Ortega, J. Toeplitz operators with quasi-separately radial symbols on the complex projective space. Bol. Soc. Mat. Mex. 22, 213–227 (2016). https://doi.org/10.1007/s40590-015-0073-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40590-015-0073-7