On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

Abstract

A bounded linear operator $T$ on a Hilbert space $\mathscr{H}$, satisfying ${\Vert T^{2}h\Vert }^2+{\Vert h\Vert }^2\ge 2{\Vert Th\Vert }^2$ for every $h\in \mathscr{H}$, is called a convex operator. In this paper, we give necessary and sufficient conditions under which a convexcomposition operator on a large class of weighted Hardy spaces is an isometry. Also, we discuss convexity of multiplication operators.