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On convexity of composition and multiplication operators on weighted Hardy spaces. (English) Zbl 1191.47040
Summary: A bounded linear operator $T$ on a Hilbert space $\Bbb H$, satisfying $\Vert T^{2}h\Vert^2+\Vert h\Vert ^{2}\geq 2\Vert Th\Vert^2$ for every $h\in \Bbb H$, 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.

MSC:
 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 46E20 Hilbert spaces of continuous, differentiable or analytic functions 47B33 Composition operators
Keywords:
weighted Hardy space
Full Text:
References:
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