Seddighin, Morteza Antieigenvalues and total antieigenvalues of normal operators. (English) Zbl 1020.47020 J. Math. Anal. Appl. 274, No. 1, 239-254 (2002). 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. Reviewer: Joe Howard (Portales/New Mexico) Cited in 7 Documents MSC: 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.) 47A12 Numerical range, numerical radius Keywords:normal operator; Banach space; first antieigenvalue; semi-inner product PDF BibTeX XML Cite \textit{M. Seddighin}, J. Math. Anal. Appl. 274, No. 1, 239--254 (2002; Zbl 1020.47020) Full Text: DOI OpenURL References: [1] Gustafson, K., The angle of an operator and positive operator products, Bull. amer. math. soc., 74, 492-499, (1968) · Zbl 0172.40702 [2] Gustafson, K., Positive (noncommuting) operators and semigroups, Math. Z., 105, 160-172, (1968) · Zbl 0159.43403 [3] Gustafson, K., A MIN-MAX theorem, Notices amer. math. soc., 15, 799, (1968) [4] Gustafson, K., Antieigenvalue inequalities in operator theory, (), 115-119 [5] Gustafson, K., An extended operator trigonometry, J. linear algebra appl., 319, 117-135, (2000) · Zbl 0969.15013 [6] Gustafson, K.; Rao, D., Numerical range and accretivity of operator products, J. math. anal. appl., 60, 693-702, (1977) · Zbl 0362.47001 [7] Gustafson, K.; Rao, D., Numerical range, (1997), Springer Berlin [8] Gustafson, K.; Seddighin, M., Antieigenvalue bounds, J. math. anal. appl., 143, 327-340, (1989) · Zbl 0696.47004 [9] Gustafson, K.; Seddighin, M., A note on total antieigenvectors, J. math. anal. appl., 178, 603-611, (1993) · Zbl 0803.47008 [10] Kantorovich, L., Functional analysis and applied mathematics, Uspekhi mat. nauk, 3, 6, 89-185, (1948) · Zbl 0034.21203 [11] Krein, N., Angular localization of the spectrum of a multiplicative integral in a Hilbert space, Functional anal. appl., 3, 89-90, (1969) [12] Rudin, W., Functional analysis, (1974), McGraw-Hill New York This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.