Norm estimates for selfadjoint Toeplitz operators on the Fock space

TL;DR

This paper derives bounds for the norm of selfadjoint Toeplitz operators with radial, bounded, and integrable symbols on the Fock space, highlighting that their operator norm is strictly less than the symbol's supremum, with implications for time-frequency localization.

Contribution

It provides a new estimate for the norm of selfadjoint Toeplitz operators with radial symbols, showing they are strictly less than the supremum norm, and explores consequences for localization operators.

Findings

Operator norm is strictly less than the supremum norm of the symbol.

The estimate applies to radial, bounded, and integrable symbols.

Implications for time-frequency localization operators are discussed.

Abstract

An estimate for the norm of selfadjoint Toeplitz operators with a radial, bounded and integrable symbol is obtained. This emphasizes the fact that the norm of such operator is strictly less than the supremum norm of the symbol. Consequences for time-frequency localization operators are also given.