Details
| Original language | English |
|---|---|
| Pages (from-to) | 271-300 |
| Number of pages | 30 |
| Journal | Integral Equations and Operator Theory |
| Volume | 78 |
| Issue number | 2 |
| Publication status | Published - 30 Oct 2013 |
| Externally published | Yes |
Abstract
We study the so-called radial operators, and in particular radial Toeplitz operators, acting on the standard weighted Bergman space on the unit ball in ℂn. They turn out to be diagonal with respect to the standard monomial basis, and the elements of their eigenvalue sequences depend only on the length of multi-indexes enumerating basis elements. We explicitly characterize the eigenvalue sequences of radial Toeplitz operators by giving a solution for the weighted extension of the classical Hausdorff moment problem, and show that the norm closure of the set of all radial Toeplitz operators with bounded measurable radial symbols coincides with the C*-algebra generated by these Toeplitz operators and is isomorphic and isometric to the C*-algebra of sequences that slowly oscillate in the sense of Schmidt.
Keywords
- slowly oscillating sequences, Toeplitz operator, Weighted Hausdorff moment problem
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Algebra and Number Theory
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In: Integral Equations and Operator Theory, Vol. 78, No. 2, 30.10.2013, p. 271-300.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Eigenvalue Characterization of Radial Operators on Weighted Bergman Spaces Over the Unit Ball
AU - Bauer, Wolfram
AU - Yañez, Crispin Herrera
AU - Vasilevski, Nikolai
N1 - Funding Information: The first named author has been supported by an “Emmy-Noether scholarship” of DFG (Deutsche Forschungsgemeinschaft). The third named author has been partially supported by CONACYT Project 102800, México. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2013/10/30
Y1 - 2013/10/30
N2 - We study the so-called radial operators, and in particular radial Toeplitz operators, acting on the standard weighted Bergman space on the unit ball in ℂn. They turn out to be diagonal with respect to the standard monomial basis, and the elements of their eigenvalue sequences depend only on the length of multi-indexes enumerating basis elements. We explicitly characterize the eigenvalue sequences of radial Toeplitz operators by giving a solution for the weighted extension of the classical Hausdorff moment problem, and show that the norm closure of the set of all radial Toeplitz operators with bounded measurable radial symbols coincides with the C*-algebra generated by these Toeplitz operators and is isomorphic and isometric to the C*-algebra of sequences that slowly oscillate in the sense of Schmidt.
AB - We study the so-called radial operators, and in particular radial Toeplitz operators, acting on the standard weighted Bergman space on the unit ball in ℂn. They turn out to be diagonal with respect to the standard monomial basis, and the elements of their eigenvalue sequences depend only on the length of multi-indexes enumerating basis elements. We explicitly characterize the eigenvalue sequences of radial Toeplitz operators by giving a solution for the weighted extension of the classical Hausdorff moment problem, and show that the norm closure of the set of all radial Toeplitz operators with bounded measurable radial symbols coincides with the C*-algebra generated by these Toeplitz operators and is isomorphic and isometric to the C*-algebra of sequences that slowly oscillate in the sense of Schmidt.
KW - slowly oscillating sequences
KW - Toeplitz operator
KW - Weighted Hausdorff moment problem
UR - http://www.scopus.com/inward/record.url?scp=84893700085&partnerID=8YFLogxK
U2 - 10.1007/s00020-013-2101-1
DO - 10.1007/s00020-013-2101-1
M3 - Article
AN - SCOPUS:84893700085
VL - 78
SP - 271
EP - 300
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 2
ER -