Commutators of weighted composition operators
- 주제(키워드) Commutator , weighted composition operator , commutant , compact operator
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 WORLD SCIENTIFIC PUBL CO PTE LTD
- 발행년도 2014
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000109668
- 본문언어 영어
- Published As http://dx.doi.org/10.1142/S0129167X14500530
초록/요약
In this paper, we prove that if the composition symbols phi and psi are linear fractional non-automorphisms of D such that phi(zeta) and psi(zeta) belong to partial derivative D for some zeta is an element of partial derivative D and u, v is an element of H-infinity are continuous on partial derivative D with u(zeta)v(zeta) not equal 0, then [W-v,W- psi*, W-u,W-phi] is compact on H-2 if and only if zeta is the common boundary fixed point of phi and psi and one of the following statements holds: (i) both phi and psi are parabolic; (ii) both phi and psi are hyperbolic and another fixed point of phi is 1/(w) over bar w where w is the fixed point of psi other than zeta. We also study the commutant of a weighted composition operator on H-2. We verify that if phi is an analytic self-map of D with Denjoy-Wolff point b is an element of D and u is an element of H-infinity\{0}, then every weighted composition operator in the commutant {W-u,W-phi}' has {f is an element of H-2 : f(b) = 0} as its nontrivial invariant subspace.
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