On convexity of composition and multiplication operators on weighted Hardy spaces
Summary: A bounded linear operator \(T\) on a Hilbert space \(\mathbb H\), satisfying \(\| T^{2}h\|^2+\| h\| ^{2}\geq 2\| Th\|^2\) for every \(h\in \mathbb H\), 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.
scientific article; zbMATH DE number 5690915
scientific article