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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Numerical range for certain classes of operators


Author: Richard Bouldin
Journal: Proc. Amer. Math. Soc. 34 (1972), 203-206
MSC: Primary 47A10
DOI: https://doi.org/10.1090/S0002-9939-1972-0293424-X
MathSciNet review: 0293424
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Abstract: We prove a basic result which relates the structure of the spectrum to the interior of the numerical range. Using this result we derive corollaries concerning compact operators, quasinilpotents, and finite dimensional operators. In particular, we characterize finite dimensional convexoid operators.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293424-X
Keywords: Hilbert space operator, numerical range, eigenvalues, convex set, extreme points, closed range
Article copyright: © Copyright 1972 American Mathematical Society