Details
| Original language | English |
|---|---|
| Pages (from-to) | 593-630 |
| Number of pages | 38 |
| Journal | Complex Analysis and Operator Theory (CAOT) |
| Volume | 9 |
| Issue number | 3 |
| Publication status | Published - 18 May 2014 |
| Externally published | Yes |
Abstract
Extending our results in Bauer and Vasilevski (J Funct Anal 265(11):2956–2990, 2013) the present paper gives a detailed structural analysis of a class of commutative Banach algebras Bk(h) generated by Toeplitz operators on the standard weighted Bergman spaces Aλ2(Bn) over the complex unit ball Bn in Cn. In the most general situation we explicitly determine the set of maximal ideals of Bk(h) and we describe the Gelfand transform on a dense subalgebra. As an application to the spectral theory we prove the inverse closedness of algebras Bk(h) in the full algebra of bounded operators on Aλ2(Bn) for certain choices of h. Moreover, it is remarked that Bk(h) is not semi-simple. In the case of k=(n) we explicitly describe the radical Rad Bn(h) of the algebraBn(h). This result generalizes and simplifies the characterization of Rad B2(1), which was given in Bauer and Vasilevski (Integr Equ Oper Theory 74:199–231, 2012).
Keywords
- Commutative Toeplitz algebra, Gelfand theory, Generalized Berezin transform, Weighted Bergman space
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Complex Analysis and Operator Theory (CAOT), Vol. 9, No. 3, 18.05.2014, p. 593-630.
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. II
T2 - Gelfand theory
AU - Bauer, Wolfram
AU - Vasilevski, Nikolai
N1 - Publisher Copyright: © 2014, Springer Basel. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2014/5/18
Y1 - 2014/5/18
N2 - Extending our results in Bauer and Vasilevski (J Funct Anal 265(11):2956–2990, 2013) the present paper gives a detailed structural analysis of a class of commutative Banach algebras Bk(h) generated by Toeplitz operators on the standard weighted Bergman spaces Aλ2(Bn) over the complex unit ball Bn in Cn. In the most general situation we explicitly determine the set of maximal ideals of Bk(h) and we describe the Gelfand transform on a dense subalgebra. As an application to the spectral theory we prove the inverse closedness of algebras Bk(h) in the full algebra of bounded operators on Aλ2(Bn) for certain choices of h. Moreover, it is remarked that Bk(h) is not semi-simple. In the case of k=(n) we explicitly describe the radical Rad Bn(h) of the algebraBn(h). This result generalizes and simplifies the characterization of Rad B2(1), which was given in Bauer and Vasilevski (Integr Equ Oper Theory 74:199–231, 2012).
AB - Extending our results in Bauer and Vasilevski (J Funct Anal 265(11):2956–2990, 2013) the present paper gives a detailed structural analysis of a class of commutative Banach algebras Bk(h) generated by Toeplitz operators on the standard weighted Bergman spaces Aλ2(Bn) over the complex unit ball Bn in Cn. In the most general situation we explicitly determine the set of maximal ideals of Bk(h) and we describe the Gelfand transform on a dense subalgebra. As an application to the spectral theory we prove the inverse closedness of algebras Bk(h) in the full algebra of bounded operators on Aλ2(Bn) for certain choices of h. Moreover, it is remarked that Bk(h) is not semi-simple. In the case of k=(n) we explicitly describe the radical Rad Bn(h) of the algebraBn(h). This result generalizes and simplifies the characterization of Rad B2(1), which was given in Bauer and Vasilevski (Integr Equ Oper Theory 74:199–231, 2012).
KW - Commutative Toeplitz algebra
KW - Gelfand theory
KW - Generalized Berezin transform
KW - Weighted Bergman space
UR - http://www.scopus.com/inward/record.url?scp=84939878285&partnerID=8YFLogxK
U2 - 10.1007/s11785-014-0385-z
DO - 10.1007/s11785-014-0385-z
M3 - Article
AN - SCOPUS:84939878285
VL - 9
SP - 593
EP - 630
JO - Complex Analysis and Operator Theory (CAOT)
JF - Complex Analysis and Operator Theory (CAOT)
SN - 1661-8254
IS - 3
ER -