Details
| Original language | English |
|---|---|
| Article number | 21 |
| Number of pages | 10 |
| Journal | Integral Equations and Operator Theory |
| Volume | 96 |
| Issue number | 3 |
| Early online date | 26 Jun 2024 |
| Publication status | Published - Sept 2024 |
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.
Keywords
- 47B65, Essential positivity, Fock space, Primary 47B35, Secondary 47B35, Toeplitz operators
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Algebra and Number Theory
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In: Integral Equations and Operator Theory, Vol. 96, No. 3, 21, 09.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Essential positivity for Toeplitz operators on the Fock space
AU - Fulsche, Robert
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024/9
Y1 - 2024/9
N2 - 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.
AB - 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.
KW - 47B65
KW - Essential positivity
KW - Fock space
KW - Primary 47B35
KW - Secondary 47B35
KW - Toeplitz operators
UR - http://www.scopus.com/inward/record.url?scp=85197175357&partnerID=8YFLogxK
U2 - 10.1007/s00020-024-02770-x
DO - 10.1007/s00020-024-02770-x
M3 - Article
AN - SCOPUS:85197175357
VL - 96
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 3
M1 - 21
ER -