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Complex Analysis and Operator Theory

, Volume 10, Issue 7, pp 1655–1677 | Cite as

Radial Toeplitz Operators on the Fock Space and Square-Root-Slowly Oscillating Sequences

  • Kevin Esmeral
  • Egor A. Maximenko
Article
  • 159 Downloads

Abstract

In this paper we show that the C*-algebra generated by radial Toeplitz operators with \(L_{\infty }\)-symbols acting on the Fock space is isometrically isomorphic to the C*-algebra of bounded sequences uniformly continuous with respect to the square-root-metric \(\rho (j,k)=|\sqrt{j}-\sqrt{k}\,|\). More precisely, we prove that the sequences of eigenvalues of radial Toeplitz operators form a dense subset of the latter C*-algebra of sequences.

Keywords

Toeplitz operator Radial Fock space Slowly oscillating sequence 

Mathematics Subject Classification

Primary 47B35 Secondary 30H20 41A35 

Notes

Acknowledgments

The authors are grateful to Professor Nikolai Vasilevski for introducing to us the world of commutative C*-algebras of Toeplitz operators. Many ideas used in the proofs come from our joint papers with Crispin Herrera Yañez, Ondrej Hutník, and Nikolai Vasilevski. The authors were partially supported by Universidad de Sucre (Colombia), by CONACYT Project 238630 (Mexico) and by the project IPN-SIP 2016-0733 (Mexico). The authors wish to express our gratitude to the referee for some helpful comments and suggestions. In particular, we included the simplified proof of Lemma 2.4 purposed by the referee (our original proof was more complicated).

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversidad de SucreSincelejoColombia
  2. 2.Escuela Superior de Física y MatemáticasInstituto Politécnico NacionalCiudad de MéxicoMexico

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