Trace formulas and $p$-essentially normal properties of quotient modules on the bidisk
Journal article, 2012
Let M be an invariant subspace of the multiplication operators M-z and M-w on the Hardy or Bergman space on D-2 = {(z,w) : |z|, |w| < 1}, and S-f = PM perpendicular to MfPM perpendicular to be the compressions on the quotient module M-perpendicular to of the multiplication operators M-f. We study the Schatten-von Neumann, in particular trace and weak trace class, properties of commutators [S-f*, S-f], and we prove the trace formulas for the commutators. Similar trace formulas for Hankel type operators are also obtained.
Hilbert module
trace class
quotient module
essentially normal quotient
k-homology
hankel-operators
reproducing kernels
spaces
normal hilbert modules
commutators
extensions
Hilbert-Schmidt class
Author
K. Y. Guo
Fudan University
K. Wang
Fudan University
Genkai Zhang
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
Journal of Operator Theory
0379-4024 (ISSN)
Vol. 67 2 511-535Subject Categories
Mathematics