On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

Hedayatian, Karim; Karimi, Lotfollah
January 2009
Abstract & Applied Analysis;2009, Special section p1
Academic Journal
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.


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