Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 199-231 |
| Seitenumfang | 33 |
| Fachzeitschrift | Integral Equations and Operator Theory |
| Jahrgang | 74 |
| Ausgabenummer | 2 |
| Publikationsstatus | Veröffentlicht - 21 Juli 2012 |
| Extern publiziert | Ja |
Abstract
Let Aλ2(Bn) denote the standard weighted Bergman space over the unit ball Bn in ℂn New classes of commutative Banach algebras T(λ) which are generated by Toeplitz operators on Aλ2(Bn) have been recently discovered in Vasilevski (Integr Equ Oper Theory 66(1):141-152, 2010). These algebras are induced by the action of the quasi-elliptic group of biholomorphisms of Bn In the present paper we analyze in detail the internal structure of such an algebra in the lowest dimensional case n = 2. We explicitly describe the maximal ideal space and the Gelfand map of T (λ). Since T (λ) is not invariant under the *-operation of L(Aλ2(Bn)) its inverse closedness is not obvious and is proved. We remark that the algebra T(λ) is not semi-simple and we derive its radical. Several applications of our results are given and, in particular, we conclude that the essential spectrum of elements in T(λ) is always connected.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Integral Equations and Operator Theory, Jahrgang 74, Nr. 2, 21.07.2012, S. 199-231.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On The Structure of A Commutative Banach Algebra Generated By Toeplitz Operators With Quasi-Radial Quasi-Homogeneous Symbols
AU - Bauer, Wolfram
AU - Vasilevski, Nikolai
N1 - Funding Information: W. Bauer has been supported by an “Emmy-Noether scholarship” of Forschungsgemeinschaft). N. Vasilevski has been partially supported Project 102800, México. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2012/7/21
Y1 - 2012/7/21
N2 - Let Aλ2(Bn) denote the standard weighted Bergman space over the unit ball Bn in ℂn New classes of commutative Banach algebras T(λ) which are generated by Toeplitz operators on Aλ2(Bn) have been recently discovered in Vasilevski (Integr Equ Oper Theory 66(1):141-152, 2010). These algebras are induced by the action of the quasi-elliptic group of biholomorphisms of Bn In the present paper we analyze in detail the internal structure of such an algebra in the lowest dimensional case n = 2. We explicitly describe the maximal ideal space and the Gelfand map of T (λ). Since T (λ) is not invariant under the *-operation of L(Aλ2(Bn)) its inverse closedness is not obvious and is proved. We remark that the algebra T(λ) is not semi-simple and we derive its radical. Several applications of our results are given and, in particular, we conclude that the essential spectrum of elements in T(λ) is always connected.
AB - Let Aλ2(Bn) denote the standard weighted Bergman space over the unit ball Bn in ℂn New classes of commutative Banach algebras T(λ) which are generated by Toeplitz operators on Aλ2(Bn) have been recently discovered in Vasilevski (Integr Equ Oper Theory 66(1):141-152, 2010). These algebras are induced by the action of the quasi-elliptic group of biholomorphisms of Bn In the present paper we analyze in detail the internal structure of such an algebra in the lowest dimensional case n = 2. We explicitly describe the maximal ideal space and the Gelfand map of T (λ). Since T (λ) is not invariant under the *-operation of L(Aλ2(Bn)) its inverse closedness is not obvious and is proved. We remark that the algebra T(λ) is not semi-simple and we derive its radical. Several applications of our results are given and, in particular, we conclude that the essential spectrum of elements in T(λ) is always connected.
KW - commutativeBanach algebra
KW - Gelfand theory
KW - quasi-homogeneous
KW - quasi-radial
KW - radical
KW - Toeplitz operator
KW - weighted Bergman space
UR - http://www.scopus.com/inward/record.url?scp=84867579604&partnerID=8YFLogxK
U2 - 10.1007/s00020-012-1987-3
DO - 10.1007/s00020-012-1987-3
M3 - Article
AN - SCOPUS:84867579604
VL - 74
SP - 199
EP - 231
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 2
ER -