Abstract and Applied Analysis
Volume 2009 (2009), Article ID 931020, 9 pages
doi:10.1155/2009/931020
Research Article

On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

Karim Hedayatian and Lotfollah Karimi

Department of Mathematics, Shiraz University, Shiraz 71454, Iran

Received 30 September 2009; Revised 2 November 2009; Accepted 4 November 2009

Academic Editor: Stevo Stević

Copyright © 2009 Karim Hedayatian and Lotfollah Karimi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.