Details
| Original language | English |
|---|---|
| Pages (from-to) | 2956-2990 |
| Number of pages | 35 |
| Journal | Journal of functional analysis |
| Volume | 265 |
| Issue number | 11 |
| Publication status | Published - 23 Aug 2013 |
| Externally published | Yes |
Abstract
Extending recent results in [3] to the higher dimensional setting n≥. 3 we provide a further step in the structural analysis of a class of commutative Banach algebras generated by Toeplitz operators on the standard weighted Bergman space over the n-dimensional complex unit ball. The algebras Bk(h) under study are subordinated to the quasi-elliptic group of automorphisms of Bn and in terms of their generators they were described in [23]. We show that Bk(h) is generated in fact by an essentially smaller set of operators, i.e., the Toeplitz operators with k-quasi-radial symbols and a finite set of Toeplitz operators with "elementary" k-quasi-homogeneous symbols. Then we analyze the structure of the commutative subalgebras corresponding to these two types of generating symbols. In particular, we describe spectra, joint spectra, maximal ideal spaces and the Gelfand transform.
Keywords
- Commutative Toeplitz algebra, Gelfand theory, Weighted Bergman space
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Journal of functional analysis, Vol. 265, No. 11, 23.08.2013, p. 2956-2990.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the structure of commutative Banach algebras generated by Toeplitz operators on the unit ball. Quasi-elliptic case. I
T2 - Generating subalgebras
AU - Bauer, Wolfram
AU - Vasilevski, Nikolai
N1 - Funding information: The first named author has been supported by an “Emmy–Noether scholarship” of DFG (Deutsche Forschungsgemeinschaft) . The second named author has been partially supported by CONACYT Project 102800 , México.
PY - 2013/8/23
Y1 - 2013/8/23
N2 - Extending recent results in [3] to the higher dimensional setting n≥. 3 we provide a further step in the structural analysis of a class of commutative Banach algebras generated by Toeplitz operators on the standard weighted Bergman space over the n-dimensional complex unit ball. The algebras Bk(h) under study are subordinated to the quasi-elliptic group of automorphisms of Bn and in terms of their generators they were described in [23]. We show that Bk(h) is generated in fact by an essentially smaller set of operators, i.e., the Toeplitz operators with k-quasi-radial symbols and a finite set of Toeplitz operators with "elementary" k-quasi-homogeneous symbols. Then we analyze the structure of the commutative subalgebras corresponding to these two types of generating symbols. In particular, we describe spectra, joint spectra, maximal ideal spaces and the Gelfand transform.
AB - Extending recent results in [3] to the higher dimensional setting n≥. 3 we provide a further step in the structural analysis of a class of commutative Banach algebras generated by Toeplitz operators on the standard weighted Bergman space over the n-dimensional complex unit ball. The algebras Bk(h) under study are subordinated to the quasi-elliptic group of automorphisms of Bn and in terms of their generators they were described in [23]. We show that Bk(h) is generated in fact by an essentially smaller set of operators, i.e., the Toeplitz operators with k-quasi-radial symbols and a finite set of Toeplitz operators with "elementary" k-quasi-homogeneous symbols. Then we analyze the structure of the commutative subalgebras corresponding to these two types of generating symbols. In particular, we describe spectra, joint spectra, maximal ideal spaces and the Gelfand transform.
KW - Commutative Toeplitz algebra
KW - Gelfand theory
KW - Weighted Bergman space
UR - http://www.scopus.com/inward/record.url?scp=84883815825&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2013.08.006
DO - 10.1016/j.jfa.2013.08.006
M3 - Article
AN - SCOPUS:84883815825
VL - 265
SP - 2956
EP - 2990
JO - Journal of functional analysis
JF - Journal of functional analysis
SN - 0022-1236
IS - 11
ER -