Abstract
Given an operator A on a Hilbert space H and c G H, we consider operators Lambda(A,c) defined on analytic functions f by Lambda(A,c)f = f (A)c. Special cases of Lambda(A,c) include vectorial Hankel operators, Carleson embeddings and weighted composition operators. For certain A, we determine conditions under which Lambda(A,c) extends to an operator of Schatten von-Neumann class on the Hardy or Bergman space of the disc. These conditions involve only the action of Lambda(A,c) on reproducing kernels and their derivatives. We also give corresponding results for operators on the Hardy space of the half-plane.
| Original language | English |
|---|---|
| Pages (from-to) | 349-371 |
| Number of pages | 23 |
| Journal | Journal of Operator Theory |
| Volume | 55 |
| Issue number | 2 |
| Publication status | Published - 2006 |
Keywords
- Schatten classes
- reproducing kernels
- Hardy space
- Bergman space
- Hankel operators
- Carleson embeddings
- composition operators
- WEISS CONJECTURE