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The boundary of the numerical range

Published online by Cambridge University Press:  18 May 2009

G. de Barra
G. de Barra
Affiliation:
Department of Mathematics, Royal Holloway College, Eghanm Surrey, U.K.
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In [1] it was shown that for a compact normal operator on a Hilbert space the numerical range was the convex hull of the point spectrum. Here it is shown that the same holds for a semi-normal operator whose point spectrum satisfies a density condition (Theorem 1). In Theorem 2 a similar condition is shown to imply that the numerical range of a semi-normal operator is closed. Some examples are given to indicate that the condition in Theorem 1 cannot be relaxed too much.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 1 , January 1981 , pp. 69 - 72
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

REFERENCES

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