Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 493-524 |
| Seitenumfang | 32 |
| Fachzeitschrift | Complex Analysis and Operator Theory |
| Jahrgang | 13 |
| Ausgabenummer | 2 |
| Frühes Online-Datum | 25 Aug. 2018 |
| Publikationsstatus | Veröffentlicht - 13 März 2019 |
Abstract
We study C ∗ -algebras generated by Toeplitz operators acting on the standard weighted Bergman space Aλ2(Bn) over the unit ball B n in C n . The symbols f ac of generating operators are assumed to be of a certain product type, see (1.1). By choosing a and c in different function algebras S a and S c over lower dimensional unit balls B ℓ and B n - ℓ , respectively, and by assuming the invariance of a∈ S a under some torus action we obtain C ∗ -algebras T λ (S a , S c ) of whose structural properties can be described. In the case of k-quasi-radial functions S a and bounded uniformly continuous or vanishing oscillation symbols S c we describe the structure of elements from the algebra T λ (S a , S c ) , derive a list of irreducible representations of T λ (S a , S c ) , and prove completeness of this list in some cases. Some of these representations originate from a “quantization effect”, induced by the representation of Aλ2(Bn) as the direct sum of Bergman spaces over a lower dimensional unit ball with growing weight parameter. As an application we derive the essential spectrum and index formulas for matrix-valued operators.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Computational Mathematics
- Informatik (insg.)
- Theoretische Informatik und Mathematik
- Mathematik (insg.)
- Angewandte Mathematik
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in: Complex Analysis and Operator Theory, Jahrgang 13, Nr. 2, 13.03.2019, S. 493-524.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Algebras of Toeplitz Operators on the n-Dimensional Unit Ball
AU - Bauer, Wolfram
AU - Hagger, Raffael
AU - Vasilevski, Nikolai
N1 - Funding Information: This work was partially supported by CONACYT Project 238630, México and by DFG (Deutsche Forschungsgemeinschaft), Project BA 3793/4-1.
PY - 2019/3/13
Y1 - 2019/3/13
N2 - We study C ∗ -algebras generated by Toeplitz operators acting on the standard weighted Bergman space Aλ2(Bn) over the unit ball B n in C n . The symbols f ac of generating operators are assumed to be of a certain product type, see (1.1). By choosing a and c in different function algebras S a and S c over lower dimensional unit balls B ℓ and B n - ℓ , respectively, and by assuming the invariance of a∈ S a under some torus action we obtain C ∗ -algebras T λ (S a , S c ) of whose structural properties can be described. In the case of k-quasi-radial functions S a and bounded uniformly continuous or vanishing oscillation symbols S c we describe the structure of elements from the algebra T λ (S a , S c ) , derive a list of irreducible representations of T λ (S a , S c ) , and prove completeness of this list in some cases. Some of these representations originate from a “quantization effect”, induced by the representation of Aλ2(Bn) as the direct sum of Bergman spaces over a lower dimensional unit ball with growing weight parameter. As an application we derive the essential spectrum and index formulas for matrix-valued operators.
AB - We study C ∗ -algebras generated by Toeplitz operators acting on the standard weighted Bergman space Aλ2(Bn) over the unit ball B n in C n . The symbols f ac of generating operators are assumed to be of a certain product type, see (1.1). By choosing a and c in different function algebras S a and S c over lower dimensional unit balls B ℓ and B n - ℓ , respectively, and by assuming the invariance of a∈ S a under some torus action we obtain C ∗ -algebras T λ (S a , S c ) of whose structural properties can be described. In the case of k-quasi-radial functions S a and bounded uniformly continuous or vanishing oscillation symbols S c we describe the structure of elements from the algebra T λ (S a , S c ) , derive a list of irreducible representations of T λ (S a , S c ) , and prove completeness of this list in some cases. Some of these representations originate from a “quantization effect”, induced by the representation of Aλ2(Bn) as the direct sum of Bergman spaces over a lower dimensional unit ball with growing weight parameter. As an application we derive the essential spectrum and index formulas for matrix-valued operators.
KW - Irreducible representations
KW - Operator C -algebra
KW - Weighted Bergman spaces
UR - http://www.scopus.com/inward/record.url?scp=85052920157&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1808.10372
DO - 10.48550/arXiv.1808.10372
M3 - Article
AN - SCOPUS:85052920157
VL - 13
SP - 493
EP - 524
JO - Complex Analysis and Operator Theory
JF - Complex Analysis and Operator Theory
SN - 1661-8254
IS - 2
ER -