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

Kevin Esmeral; Egor A. Maximenko

doi:10.1007/s11785-016-0557-0

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

Kevin Esmeral, Egor A. Maximenko

Escuela Superior de Física y Matemáticas (ESFM)

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

In this paper we show that the C*-algebra generated by radial Toeplitz operators with L_∞-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 ρ(j,k)=|j-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.

Original language	English
Pages (from-to)	1655-1677
Number of pages	23
Journal	Complex Analysis and Operator Theory
Volume	10
Issue number	7
DOIs	https://doi.org/10.1007/s11785-016-0557-0
State	Published - 1 Oct 2016

Keywords

Fock space
Radial
Slowly oscillating sequence
Toeplitz operator

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abstract = "In this paper we show that the C*-algebra generated by radial Toeplitz operators with L∞-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 ρ(j,k)=|j-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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N2 - In this paper we show that the C*-algebra generated by radial Toeplitz operators with L∞-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 ρ(j,k)=|j-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.

AB - In this paper we show that the C*-algebra generated by radial Toeplitz operators with L∞-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 ρ(j,k)=|j-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.

KW - Fock space

KW - Radial

KW - Slowly oscillating sequence

KW - Toeplitz operator

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IS - 7

ER -

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

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Keywords

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