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On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

Author

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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.

Suggested Citation

  • Karim Hedayatian & Lotfollah Karimi, 2009. "On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    • Handle: RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:931020
    DOI: 10.1155/2009/931020
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    References listed on IDEAS

    as
    1. Stevo Stević, 2008. "Essential Norms of Weighted Composition Operators from the -Bloch Space to a Weighted-Type Space on the Unit Ball," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-11, November.
    2. Sei-Ichiro Ueki & Luo Luo, 2008. "Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-12, March.
    3. Sei-Ichiro Ueki & Luo Luo, 2008. "Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    4. Stevo Stević, 2008. "Essential Norms of Weighted Composition Operators from the α‐Bloch Space to a Weighted‐Type Space on the Unit Ball," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
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    Cited by:

    1. Z. Kamali & K. Hedayatian & B. Khani Robati, 2010. "Non‐Weakly Supercyclic Weighted Composition Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Jingfeng Tian & Yang-Xiu Zhou, 2013. "Refinements of Hardy‐Type Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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