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Subspaces associated with boundary points of the numerical range

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

S. Majumdar  and
Brailey Sims
S. Majumdar
Affiliation:
University of New EnglandArmidale, N.S.W. 2351, Australia
Brailey Sims
Affiliation:
University of New EnglandArmidale, N.S.W. 2351AustraliaQueen's UniversityKingston, Ontario K7L 3N6, Canada
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Abstract

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Stampfli and Embry characterized points in the numerical range which are extreme in terms of the linearity of corresponding sets of vectors. Das and Craven generalized this to include the case of unattained boundary points. We give an alternative proof of this result using a technique of Berberian. This approach appears to be more conceptual in that it enables us to deduce the result from that of Stampfli and Embry. We also illustrate how the same technique may be used to generalize other results of Embry.

MSC classification

Secondary: 47A12: Numerical range, numerical radius
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 1 , August 1985 , pp. 21 - 27
Copyright
Copyright © Australian Mathematical Society 1985

References

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