On simplicity of the maximal eigenvalue (Q5945767)
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scientific article; zbMATH DE number 1657557
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On simplicity of the maximal eigenvalue |
scientific article; zbMATH DE number 1657557 |
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On simplicity of the maximal eigenvalue (English)
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2001
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selfadjoint compact operator
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simple maximal eigenvalue
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Let \(A\) be a selfadjoint compact operator in a Hilbert space \({\mathfrak H}\). With \(\varphi\in{\mathfrak H}\) it defined a family NEWLINE\[NEWLINEA(t)= A+ t\langle\cdot,\varphi\rangle\varphi,NEWLINE\]NEWLINE \(t\in [t_0,\infty]\). If \(t\) is sufficiently large \(A(t)\) has a simple maximal eigenvalue and the corresponding eigenvector is not orthogonal to \(\varphi\).
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