Antieigenvalues and total antieigenvalues of normal operators. (English) Zbl 1020.47020

Given an operator \(T\) on a Banach space \(X\), the first antieigenvalue of \(T\) is \[ \mu_1(T)= \inf_{Tf\neq 0} {\text{Re} (Tf,f)\over\|Tf \|\|f\|} \] where \((f,g)\) is a semi-inner product on \(X\). This paper generalizes earlier work on antieigenvalues and total antieigenvalues of normal operators.


47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47A12 Numerical range, numerical radius
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