Numerical radius of bounded operators with \(\ell^p\)-norm (Q2107435)
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scientific article; zbMATH DE number 7625860
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Numerical radius of bounded operators with \(\ell^p\)-norm |
scientific article; zbMATH DE number 7625860 |
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Numerical radius of bounded operators with \(\ell^p\)-norm (English)
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1 December 2022
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The authors consider a direct sum of Hilbert spaces \(H\) endowed with a \(p\)-norm, \(1\leq p\leq \infty\), and then introduce for a bounded linear operator \(T\) on \(H\) a set \(W_p(T)\) which they call ``numerical range''. Then they show that many properties known for the classical numerical range of a bounded linear operator in a Hilbert space carry over to \(W_p(T)\). Some of the properties depend on \(p\).
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numerical radius
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inner product
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\(\ell^p\)-sum
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direct sum of a family of Hilbert spaces
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