Toeplitz and Hankel operators and Dixmier traces on the unit ball of Cn
Journal article, 2009
We compute the Dixmier trace of pseudo-Toeplitz operators on the Fock space. As an application we find a formula for the Dixmier trace of the product of commutators of Toeplitz operators on the Hardy and weighted Bergman spaces on the unit ball of ℂd. This generalizes an earlier work of Helton-Howe for the usual trace of the anti-symmetrization of Toeplitz operators.
Hankel operators
Dixmier trace
Pseudo-Toeplitz operators
Boundary CR operators
Toeplitz operators
Schatten- von Neumann classes
Invariant Banach spaces
Pseudo-differential operators
Macaev classes
Trace
Author
M. Englis
Czech Academy of Sciences
Slezska univerzita v Opave
K. Y. Guo
Fudan University
Genkai Zhang
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Proceedings of the American Mathematical Society
0002-9939 (ISSN) 1088-6826 (eISSN)
Vol. 137 11 3669-3678Subject Categories
Mathematics
DOI
10.1090/S0002-9939-09-09331-9