Symmetric anti-eigenvalue and symmetric anti-eigenvector. (English) Zbl 1141.47016

Summary: The idea of symmetric anti-eigenvalue and symmetric anti-eigenvector of a bounded linear operator \(T\) on a Hilbert space \(H\) is introduced. The structure of symmetric anti-eigenvectors of a selfadjoint and certain classes of normal operators is found in terms of eigenvectors. The Kantorovich inequality for selfadjoint operators and bounds for symmetric anti-eigenvalues for certain classes of normal operators are also discussed.


47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47A10 Spectrum, resolvent
47A63 Linear operator inequalities
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