Self-commutators of invertible weighted composition operators on H^2
2014.07.23 16:25
| 실적년도 | 2013년 |
|---|---|
| 논문구분 | 국외 |
| 총저자 | Sungeun Jung, Eungil Ko |
| 학술지명 | Complex Variables and Elliptic Equations |
| 권(Vol.) | 59 |
| 호(No.) | 5 |
| 게재년월 | 2014년 5월 |
| Impact Factor | 0.650(jcr2013) |
| SCI 등재 | SCIE |
| 비고 |
In this paper, we consider the self-commutator of an invertible weighted
composition operator Wf, φ on the Hardy space H2 where f
is continuous on D̄. We show that both the self-commutator [Wf,φ*,
Wf,φ] and the anti-self-commutator {Wf,φ*,
Wf,φ} are expressed as compact perturbations of Toeplitz operators.
Moreover, we give an alternative proof for the result in 2 that
Wf,φ is unitary exactly when φ is an automorphism of D and (Formula
presented.) where p = φ-1(0), Kp is the reproducing kernel
at p for H2, and c is a constant with {pipe}c{pipe} = 1. We next show
that when {pipe}f(z){pipe} ≤ {pipe}f(φ(z)){pipe} for all z ∈ D, the weighted
composition operator Wf,φ is normal if and only if the composition
operator Cφ is unitary and f is constant on D. We also provide some
spectral properties of Wf,φ* Wf,φ and Wf,φ
Wf,φ*.
