- Thursday, January 1, 1998
- On Composition Operators on N+(&Omega;)
- Published at:An-Najah Univ. J. Res., Vol. 12, (1998) 21-28
Let N(Ω) denote the class of analytic functions fin a domain Ω, contained in the complex numbers C, such that log(1+| f |) has a harmonic majorant. The subclass N+(Ω) of N(Ω) consists of all f such that log(1+| f |) has a quasi-bounded harmonic majorant. Let Φ be a non-constant analytic function from Ω into itself Define the composition operator CΦ, on N(Ω) by CΦf=foΦ, V f € N(Ω). Then CΦ, maps N+(Ω) into itself. Here we characterize the invertibility of CΦ when Ω is finitely connected with boundary Γ consisting of disjoint analytic simple closed curves and we give a necessary condition for the density of the range of CΦ, in N+(Ω). Moreover, we consider linear isometries on N+(Ω) and their relation to CΦ .