Upper bounds for the Euclidean operator radius and applications (Q1008468)
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scientific article; zbMATH DE number 5534601
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Upper bounds for the Euclidean operator radius and applications |
scientific article; zbMATH DE number 5534601 |
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Upper bounds for the Euclidean operator radius and applications (English)
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30 March 2009
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The Euclidean operator radius of an \(n\)-tuple \((T_1,\dots,T_n)\) of bounded linear operators on a Hilbert space is defined by \(w_e(T_1,\dots,T_n) = \sup_{\|h\|=1} \left(\sum_{i=1}^n |(T_ih,h)|^2\right)^{1/2}\). The paper under review establishes sharp upper bounds for \(w_e\). The tools used are several generalizations of the Bessel inequality due to Boas-Bellman, Bombieri, and the author himself.
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Euclidean operator radius
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numerical radius
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numerical range
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Bessel inequality
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Boas-Bellman-type inequalities
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Bombieri-type inequalities
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