On a class of ideals of the Toeplitz algebra on the Bergman space
Author:
Trieu Le
Journal:
Proc. Amer. Math. Soc. 136 (2008), 3571-3577
MSC (2000):
Primary 47B35; Secondary 47B47
DOI:
https://doi.org/10.1090/S0002-9939-08-09569-5
Published electronically:
June 6, 2008
MathSciNet review:
2415041
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let denote the full Toeplitz algebra on the Bergman space of the unit ball
. For each subset
of
, let
denote the closed two-sided ideal of
generated by all
with
. It is known that
, the ideal of compact operators, and
. Despite these ``extreme cases'', there are subsets
of
so that
. This paper gives a construction of a class of such subsets.
- [1] Lewis A. Coburn, Singular integral operators and Toeplitz operators on odd spheres, Indiana Univ. Math. J. 23 (1973/74), 433-439. MR 0322595 (48:957)
- [2]
Trieu Le, On the commutator ideal of the Toeplitz algebra on the Bergman space of the unit ball in
, J. Operator Theory, to appear.
- [3] Young J. Lee, Pluriharmonic symbols of commuting Toeplitz type operators on the weighted Bergman spaces, Canad. Math. Bull. 41 (1998), no. 2, 129-136. MR 1624149 (99b:47035)
- [4]
Walter Rudin, Function theory in the unit ball of
, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241, Springer-Verlag, New York, 1980. MR 601594 (82i:32002)
- [5] Daniel Suárez, The Toeplitz algebra on the Bergman space coincides with its commutator ideal, J. Operator Theory 51 (2004), no. 1, 105-114. MR 2055807 (2005b:47060)
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Additional Information
Trieu Le
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email:
trieu.le@utoronto.edu
DOI:
https://doi.org/10.1090/S0002-9939-08-09569-5
Received by editor(s):
August 16, 2007
Published electronically:
June 6, 2008
Communicated by:
Marius Junge
Article copyright:
© Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.