Surjective Isometries of Multiplication Operators and Weighted Composition Operators on nth Weighted-Type Banach Spaces of Analytic Functions

Abstract

This paper is to characterize isometries of multiplication operators and weighted composition operators on the nth weighted-type Banach spaces {V_n : n ∈ N} of analytic functions on the open unit disk of which the Bloch space and the Zygmund space are particular cases at n = 1, 2. We give characterizations of the symbols ψ and φ for which the multiplication operator M_ψ and the weighted composition operator W_ψ,φ are surjective isometries. Moreover, we show that generalized weighted composition operators are not isometric on V_n.