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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.

Information

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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