Essential positivity for Toeplitz operators on the Fock space

verfasst von

Robert Fulsche

Abstract

In this short note, we discuss essential positivity of Toeplitz operators on the Fock space, as motivated by a recent question of Perälä and Virtanen (Proc. Amer. Math. Soc. 151:4807–4815, 2023). We give a proper characterization of essential positivity in terms of limit operators. A conjectured characterization of essential positivity of Perälä and Virtanen is disproven when the assumption of radiality is dropped. Nevertheless, when the symbol of the Toeplitz operator is of vanishing mean oscillation, we show that the conjecture of Perälä and Virtanen holds true, even without radiality.

Organisationseinheit(en)

Institut für Analysis

Typ

Artikel

Journal

Integral Equations and Operator Theory

Band

96

Anzahl der Seiten

10

ISSN

0378-620X

Publikationsdatum

09.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Analysis, Algebra und Zahlentheorie

Elektronische Version(en)

https://doi.org/10.1007/s00020-024-02770-x (Zugang: Offen)