Normal essential eigenvalues in the boundary of the numerical range
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- by Norberto Salinas and Maria Victoria Velasco PDF
- Proc. Amer. Math. Soc. 129 (2001), 505-513 Request permission
Abstract:
A purely geometric property of a point in the boundary of the numerical range of an operator $T$ on Hilbert space is examined which implies that such a point is the value at $T$ of a multiplicative linear functional of the $C^*$-algebra, $C^*(T)$, generated by $T$ and the identity operator. Roughly speaking, such a property means that the boundary of the numerical range (of $T$) has infinite curvature at that point. Furthermore, it is shown that if such a point is not a sharp linear corner of the numerical range of $T$, then the multiplicative linear functional vanishes on the compact operators in $C^*(T)$.References
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Additional Information
- Norberto Salinas
- Affiliation: Department of Mathematics, The University of Kansas, Lawrence, Kansas 66045
- Email: norberto@kuhub.cc.ukans.edu
- Maria Victoria Velasco
- Affiliation: Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain
- Email: vvelasco@goliat.ugr.es
- Received by editor(s): November 30, 1998
- Received by editor(s) in revised form: April 29, 1999
- Published electronically: October 12, 2000
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 505-513
- MSC (1991): Primary 47A12
- DOI: https://doi.org/10.1090/S0002-9939-00-05933-5
- MathSciNet review: 1800238