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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.

47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
46E20Hilbert spaces of continuous, differentiable or analytic functions
47B33Composition operators
Full Text: DOI EuDML
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