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The numerical ranges of unbounded linear operators

Published online by Cambridge University Press:  17 April 2009

Béla Bollobás  and
Stephan E. Eldridge
Béla Bollobás
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, England.
Stephan E. Eldridge
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, England.
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Abstract

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Giles and Joseph (Bull. Austral. Math. Soc. 11 (1974), 31–36), proved that the numerical range of an unbounded operator on a Banach space has a certain density property. They showed, in particular, that the numerical range of an unbounded operator on certain Banach spaces is dense in the scalar field. We prove that the numerical range of an unbounded operator on a Banach space is always dense in the scalar field.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1975 , pp. 23 - 25
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Giles, J.R. and Joseph, G., “The numerical ranges of unbounded operators”, Bull. Austral. Math. Soc. 11 (1974), 31–36.CrossRefGoogle Scholar