On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

Abstract

A bounded linear operator T on a Hilbert space ℋ, satisfying ‖T2h‖2+‖h‖2≥2‖Th‖2 for every h∈ℋ, is called a convex operator. In this paper, we give necessary and sufficient conditions under which a convex composition operator on a large class of weighted Hardy spaces is an isometry. Also, we discuss convexity of multiplication operators.