We present some properties of mixture and generalized mixture operators, with special stress on their monotonicity. We introduce new sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. However, mixture operators, generalized mixture operators neither quasi-arithmetic means weighted by a weighting function need not be non-decreasing operators,...

Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb (G, E) and HV0 (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings φ : G → G and operator-valued analytic mappings Ψ : G → B (E) whi...

We determine the spectra of weighted composition operators acting on the weighted Banach spaces of analytic functions H∞ vp when the symbol φ has a fixed point in the open unit disk. Further, we apply this result to give the spectra of composition operators on Bloch type spaces. In particular, we answer in the affirmative a conjecture by MacCluer and Saxe.

In this paper, we study the weighted composition operators Wφ,ψ :f → ψ(f ◦ φ) between weighted Bergman spaces and Hardy spaces on the unit ball of Cn. We characterize the boundedness and the compactness of the weighted composition operators Wφ,ψ :Ap(να)→Aq(νβ) (0 < q < p <∞, −1 < α,β <∞) and Wφ,ψ :Hp(B)→Hq(B) (0 < q < p <∞). © 2006 Elsevier Inc. All rights reserved.