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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Normal essential eigenvalues in the boundary of the numerical range


Authors: Norberto Salinas and Maria Victoria Velasco
Journal: Proc. Amer. Math. Soc. 129 (2001), 505-513
MSC (1991): Primary 47A12
Published electronically: October 12, 2000
MathSciNet review: 1800238
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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 $C^*(T)$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05933-5
PII: S 0002-9939(00)05933-5
Keywords: Infinite curvature, eigenvalue.
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
Article copyright: © Copyright 2000 American Mathematical Society