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

DOI:
https://doi.org/10.1090/S0002-9939-00-05933-5

Published electronically:
October 12, 2000

MathSciNet review:
1800238

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Abstract | References | Similar Articles | Additional Information

Abstract: A purely geometric property of a point in the boundary of the numerical range of an operator on Hilbert space is examined which implies that such a point is the value at of a multiplicative linear functional of the -algebra, , generated by and the identity operator. Roughly speaking, such a property means that the boundary of the numerical range (of ) 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 , then the multiplicative linear functional vanishes on the compact operators in .

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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:
https://doi.org/10.1090/S0002-9939-00-05933-5

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