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On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

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  • Karim Hedayatian
  • Lotfollah Karimi

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.

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Handle: RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:931020
DOI: 10.1155/2009/931020
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