Normal essential eigenvalues in the boundary of the numerical range |
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| Authors: | Norberto Salinas Maria Victoria Velasco |
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| Institution: | Department of Mathematics, The University of Kansas, Lawrence, Kansas 66045 ; Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain |
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| 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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| Keywords: | Infinite curvature eigenvalue |
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