Essential positivity for Toeplitz operators on the Fock space

authored by

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.

Organisation(s)

Institute of Analysis

Type

Article

Journal

Integral Equations and Operator Theory

Volume

96

No. of pages

10

ISSN

0378-620X

Publication date

09.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Analysis, Algebra and Number Theory

Electronic version(s)

https://doi.org/10.1007/s00020-024-02770-x (Access: Open)