## Abstract and Applied Analysis

### On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

#### Abstract

A bounded linear operator $T$ on a Hilbert space $\mathcal{H}$, satisfying ${\Vert {T}^{2}h\Vert }^{2}+{\Vert h\Vert }^{2}\geq 2{\Vert Th\Vert }^{2}$ for every $h\in \mathcal{H}$, 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 931020, 9 pages.

Dates
First available in Project Euclid: 16 March 2010

https://projecteuclid.org/euclid.aaa/1268745616

Digital Object Identifier
doi:10.1155/2009/931020

Mathematical Reviews number (MathSciNet)
MR2564003

Zentralblatt MATH identifier
1191.47040

#### Citation

Hedayatian, Karim; Karimi, Lotfollah. On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces. Abstr. Appl. Anal. 2009 (2009), Article ID 931020, 9 pages. doi:10.1155/2009/931020. https://projecteuclid.org/euclid.aaa/1268745616

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