A trace formula for multiplication operators on invariant subspaces of theBergman space

Authors
Zhu, K
Citation
K. Zhu, A trace formula for multiplication operators on invariant subspaces of theBergman space, INTEG EQ OP, 40(2), 2001, pp. 244-255
Citations number
13
Categorie Soggetti
Mathematics
Journal title
INTEGRAL EQUATIONS AND OPERATOR THEORY
ISSN journal
0378620X → ACNP
Volume
40
Issue
2
Year of publication
2001
Pages
244 - 255
Database
ISI
SICI code
0378-620X(200105)40:2<244:ATFFMO>2.0.ZU;2-2
Abstract
Suppose f is a bounded analytic function in the unit disk D and M-f is the multiplication operator on an invariant subspace I of the Bergman space. We show that tr [M-f*, M-f] = n integral (D)\f ' (z)\(2)dA(z), where n = dim(l circle minus zI).