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The numerical ranges of unbounded operators

Published online by Cambridge University Press:  17 April 2009

J.R. Giles  and
G. Joseph
J.R. Giles
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, New South Wales.
G. Joseph
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, New South Wales.
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Abstract

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On a Banach space the numerical range of an unbounded operator has a certain density property in the scalar field. Consequently all hermitian and dissipative operators are bounded. For a smooth or separable or reflexive Banach space the numerical range of an unbounded operator is dense in the scalar field.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 1 , August 1974 , pp. 31 - 36
Copyright
Copyright © Australian Mathematical Society 1974

References

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