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Subsets characterizing the closure of the numerical range

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

K. C. Das ,
S. Majumdar  and
Brailey Sims
K. C. Das
Affiliation:
Indian Institute of Technology, Karagpur 721320, India
S. Majumdar
Affiliation:
S. Majumdar and Brailey Sims, University of New England, Armidale, N.S.W. 2351, Australia
Brailey Sims
Affiliation:
S. Majumdar and Brailey Sims, University of New England, Armidale, N.S.W. 2351, Australia
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Abstract

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For an operator on a Hilbert space, points in the closure of its numerical range are characterized as either extreme, non-extreme boundary, or interior in terms of various associated sets of bounded sequences of vectors. These generalize similar results due to Embry, for points in the numerical range.

MSC classification

Secondary: 47A12: Numerical range, numerical radius
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 1 , February 1986 , pp. 1 - 4
Copyright
Copyright © Australian Mathematical Society 1986

References

Das, K. C. and Craven, B. D. (1983), ‘Linearity and weak convergence on the boundary of numerical range’, J. Austral. Math. Soc. Ser. A 35, 221–226.CrossRefGoogle Scholar
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Embry, M. R. (1975), ‘Orthogonality and the numerical range,’ J. Math. Sol. Japan 27, 405–411.Google Scholar
Halmos, P. R. (1967), Hilbert space problem book (Van Nostrand, New York).Google Scholar
Majumdar, S. and Sims, B. (to appear), ‘Subspaces associated with boundary points of the numerical range’, J. Austral. Math. Soc. Ser. A.Google Scholar
Stampfil, J. G. (1966), ‘Extreme points of the numerical range of a hyponormal operator’, Michigan Math. J. 13, 87–89.Google Scholar