Access the full text.
Sign up today, get DeepDyve free for 14 days.
Z. C̆uc̆ković, N. Rao (1998)
Mellin Transform, Monomial Symbols, and Commuting Toeplitz OperatorsJournal of Functional Analysis, 154
Trieu Le (2008)
The commutants of certain Toeplitz operators on weighted Bergman spacesJournal of Mathematical Analysis and Applications, 348
N. Vasilevski (2003)
Bergman Space Structure, Commutative Algebras of Toeplitz Operators, and Hyperbolic GeometryIntegral Equations and Operator Theory, 46
N. Vasilevski (2010)
Quasi-Radial Quasi-Homogeneous Symbols and Commutative Banach Algebras of Toeplitz OperatorsIntegral Equations and Operator Theory, 66
S. Grudsky, R. Quiroga-Barranco, R. Quiroga-Barranco, N. Vasilevski (2006)
Commutative C∗-algebras of Toeplitz operators and quantization on the unit diskJournal of Functional Analysis, 234
R. Quiroga-Barranco, N. Vasilevski (2007)
Commutative C ∗-algebras of Toeplitz operators on the unit ball , I . Bargmann type transforms and spectral representations of Toeplitz operators
Y. Lee (2010)
Commuting Toeplitz operators on the Hardy space of the polydisk, 138
W. Bauer, Y. Lee (2011)
Commuting Toeplitz operators on the Segal–Bargmann spaceJournal of Functional Analysis, 260
N. Vasilevski (2010)
Parabolic Quasi-radial Quasi-homogeneous Symbols and Commutative Algebras of Toeplitz Operators
B. Choe, Y. Lee (1993)
PLURIHARMONIC SYMBOLS OF COMMUTING TOEPLITZ OPERATORSIllinois Journal of Mathematics, 37
B. Choe, H. Koo, Y. Lee (2003)
Commuting Toeplitz operators on the polydiskTransactions of the American Mathematical Society, 356
[We continue the study of commutative algebras generated by Toeplitz operators acting on the weighted Bergman spaces over the unit ball Bn in Cn. As was observed recently, apart of the already known commutative Toeplitz C * -algebras, quite unexpectedly, there exist many others, not geometrically defined, classes of symbols which generate commutative Toeplitz operator algebras on each weighted Bergman space. These classes of symbols were in a sense subordinated to the quasi-elliptic and quasi-parabolic groups of biholomorphisms of the unit ball. The corresponding commutative operator algebras were Banach, and being extended to the C * -algebras they became non-commutative. We consider here the case of symbols subordinated to the quasi-hyperbolic group and show that such classes of symbols are as well the sources for the commutative Banach algebras generated by Toeplitz operators. That is, together with the results of [11, 12], we cover the multidimensional extensions of all three model cases on the unit disk.]
Published: Jan 3, 2012
Keywords: Toeplitz operator; weighted Bergman space; unit ball; commutative Banach algebra; quasi-hyperbolic group
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.