Details
| Original language | English |
|---|---|
| Pages (from-to) | 25-34 |
| Number of pages | 10 |
| Journal | Integral Equations and Operator Theory |
| Volume | 83 |
| Issue number | 1 |
| Publication status | Published - 23 Sept 2015 |
Abstract
Let Tf be a Toeplitz operator on the Segal–Bargmann space or the standard weighted Bergman space over a bounded symmetric domain Ω⊂Cn with possibly unbounded symbol f. Combining recent results in Bauer et al. (J. Funct. Anal. 259:57–78, 2010), Bauer et al. (J. reine angew. Math. doi:10.1515/crelle-2015-0016), Issa (Integr. Equ. Oper. Theory 70:569–582, 2011) we show that in the case of uniformly continuous symbols f with respect to the Euclidean metric on Cn and the Bergman metric on Ω, respectively, the operator Tf is bounded if and only if f is bounded. Moreover, Tf is compact if and only if f vanishes at the boundary of Ω. This observation substantially extends a result in Coburn (Indiana Univ. Math. J. 23:433–439, 1973).
Keywords
- Bergman metric, bounded symmetric domain, heat transform, Segal–Bargmann space
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Algebra and Number Theory
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In: Integral Equations and Operator Theory, Vol. 83, No. 1, 23.09.2015, p. 25-34.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Toeplitz Operators with Uniformly Continuous Symbols
AU - Bauer, Wolfram
AU - Coburn, Lewis A.
N1 - Publisher Copyright: © 2015, Springer Basel. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2015/9/23
Y1 - 2015/9/23
N2 - Let Tf be a Toeplitz operator on the Segal–Bargmann space or the standard weighted Bergman space over a bounded symmetric domain Ω⊂Cn with possibly unbounded symbol f. Combining recent results in Bauer et al. (J. Funct. Anal. 259:57–78, 2010), Bauer et al. (J. reine angew. Math. doi:10.1515/crelle-2015-0016), Issa (Integr. Equ. Oper. Theory 70:569–582, 2011) we show that in the case of uniformly continuous symbols f with respect to the Euclidean metric on Cn and the Bergman metric on Ω, respectively, the operator Tf is bounded if and only if f is bounded. Moreover, Tf is compact if and only if f vanishes at the boundary of Ω. This observation substantially extends a result in Coburn (Indiana Univ. Math. J. 23:433–439, 1973).
AB - Let Tf be a Toeplitz operator on the Segal–Bargmann space or the standard weighted Bergman space over a bounded symmetric domain Ω⊂Cn with possibly unbounded symbol f. Combining recent results in Bauer et al. (J. Funct. Anal. 259:57–78, 2010), Bauer et al. (J. reine angew. Math. doi:10.1515/crelle-2015-0016), Issa (Integr. Equ. Oper. Theory 70:569–582, 2011) we show that in the case of uniformly continuous symbols f with respect to the Euclidean metric on Cn and the Bergman metric on Ω, respectively, the operator Tf is bounded if and only if f is bounded. Moreover, Tf is compact if and only if f vanishes at the boundary of Ω. This observation substantially extends a result in Coburn (Indiana Univ. Math. J. 23:433–439, 1973).
KW - Bergman metric
KW - bounded symmetric domain
KW - heat transform
KW - Segal–Bargmann space
UR - http://www.scopus.com/inward/record.url?scp=84942199147&partnerID=8YFLogxK
U2 - 10.1007/s00020-015-2235-4
DO - 10.1007/s00020-015-2235-4
M3 - Article
AN - SCOPUS:84942199147
VL - 83
SP - 25
EP - 34
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 1
ER -