1. COMPACT COMPOSITION OPERATORS ON WEIGHTED HILBERT SPACES.
- Author
-
AL-RAWASHDEH, WALEED
- Subjects
NONLINEAR operators ,HILBERT space ,BERGMAN spaces ,HARDY spaces ,MATHEMATICAL functions - Abstract
Let φ be an analytic self-map of open unit disk 픽. A composition operator is defined as (C
φ f)(z) = f(φ (z)), for z ∈ 픽and f analytic on 픽. Given an admissible weight w, the weighted Hilbert space Hw consists of all analytic functions f such that ... = |f(0)|² + ∫픽 |f'(z)\²w(z)dA(z) is finite. In this paper, we study composition operators acting between weighted Bergman space Aα ² and the weighted Hilbert space Hw . Using generalized Nevalinna counting functions associated with w, we characterize the bounded-ness and compactness of these composition operators. [ABSTRACT FROM AUTHOR]- Published
- 2015