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On the convexity of Stampfli's numerical range

Published online by Cambridge University Press:  17 April 2009

J. O. Agure
J. O. Agure
Affiliation:
Kenyatta University, Mathematics Department, PO Box 43844, Nairobi, Kenya
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This paper investigates a certain type of numerical range introduced by Stampfli. In particular, we investigate the convexity of this set of elements of operators on Hilbert spaces and its relationship to the algebra numerical range implemented by elements of a W*-algebra.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 1 , February 1996 , pp. 33 - 37
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Agure, J.O., ‘On the numerical ranges and norms of derivations’, Ph.D. Thesis (University of Birmingham, England, 1992).Google Scholar
[2]Bonsall, F.F. and Duncan, J., Numerical Ranges II (Cambridge University Press, New York, 1973).CrossRefGoogle Scholar
[3]Stampfli, J.G., ‘Norms of derivations’, Pacific Journal of Mathematics 33 (1970), 737–747.CrossRefGoogle Scholar