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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, Universidad de Sucre, Sincelejo, Colombia

    Kevin Esmeral

  2. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, 07730, Ciudad de México, Mexico

    Egor A. Maximenko

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  1. Kevin Esmeral
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  2. Egor A. Maximenko
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Correspondence to Kevin Esmeral.

Additional information

Communicated by Christian Le Merdy.

The work on the paper was partically supported by Universidad de Sucre (Colombia), by CONACYT Project 238630 (Mexico) and by IPN-SIP Project 20160733 (Mexico).

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Esmeral, K., Maximenko, E.A. Radial Toeplitz Operators on the Fock Space and Square-Root-Slowly Oscillating Sequences. Complex Anal. Oper. Theory 10, 1655–1677 (2016). https://doi.org/10.1007/s11785-016-0557-0

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