## 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.

### MSC:

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