Details
| Original language | English |
|---|---|
| Pages (from-to) | 460-489 |
| Number of pages | 30 |
| Journal | Journal of functional analysis |
| Volume | 260 |
| Issue number | 2 |
| Publication status | Published - 22 Sept 2010 |
| Externally published | Yes |
Abstract
Consider two Toeplitz operators Tg, Tf on the Segal-Bargmann space over the complex plane. Let us assume that g is a radial function and both operators commute. Under certain growth condition at infinity of f and g we show that f must be radial, as well. We give a counterexample of this fact in case of bounded Toeplitz operators but a fast growing radial symbol g. In this case the vanishing commutator [Tg,Tf]=0 does not imply the radial dependence of f. Finally, we consider Toeplitz operators on the Segal-Bargmann space over Cn and n>1, where the commuting property of Toeplitz operators can be realized more easily.
Keywords
- Mellin transform, Radial symbol, Reproducing kernel Hilbert space, Toeplitz operator
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of functional analysis, Vol. 260, No. 2, 22.09.2010, p. 460-489.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Commuting Toeplitz operators on the Segal-Bargmann space
AU - Bauer, Wolfram
AU - Lee, Young Joo
N1 - Funding Information: * Corresponding author. E-mail addresses: wbauer@uni-math.gwdg.de (W. Bauer), leeyj@chonnam.ac.kr (Y.J. Lee). 1 The first named author has been supported by an “Emmy-Noether scholarship” of DFG (Deutsche Forschungs-gemeinschaft). Copyright: Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2010/9/22
Y1 - 2010/9/22
N2 - Consider two Toeplitz operators Tg, Tf on the Segal-Bargmann space over the complex plane. Let us assume that g is a radial function and both operators commute. Under certain growth condition at infinity of f and g we show that f must be radial, as well. We give a counterexample of this fact in case of bounded Toeplitz operators but a fast growing radial symbol g. In this case the vanishing commutator [Tg,Tf]=0 does not imply the radial dependence of f. Finally, we consider Toeplitz operators on the Segal-Bargmann space over Cn and n>1, where the commuting property of Toeplitz operators can be realized more easily.
AB - Consider two Toeplitz operators Tg, Tf on the Segal-Bargmann space over the complex plane. Let us assume that g is a radial function and both operators commute. Under certain growth condition at infinity of f and g we show that f must be radial, as well. We give a counterexample of this fact in case of bounded Toeplitz operators but a fast growing radial symbol g. In this case the vanishing commutator [Tg,Tf]=0 does not imply the radial dependence of f. Finally, we consider Toeplitz operators on the Segal-Bargmann space over Cn and n>1, where the commuting property of Toeplitz operators can be realized more easily.
KW - Mellin transform
KW - Radial symbol
KW - Reproducing kernel Hilbert space
KW - Toeplitz operator
UR - http://www.scopus.com/inward/record.url?scp=78049423868&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2010.09.007
DO - 10.1016/j.jfa.2010.09.007
M3 - Article
AN - SCOPUS:78049423868
VL - 260
SP - 460
EP - 489
JO - Journal of functional analysis
JF - Journal of functional analysis
SN - 0022-1236
IS - 2
ER -