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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on numerical ranges of operators
in spaces with an indefinite metric


Authors: Chi-Kwong Li and Leiba Rodman
Journal: Proc. Amer. Math. Soc. 126 (1998), 973-982
MSC (1991): Primary 15A60, 47A12, 47A37
MathSciNet review: 1443838
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Abstract: The numerical range of an operator on an indefinite inner product space (possibly infinite dimensional) is studied. In particular, operators having bounded numerical ranges are characterized, and the angle points of the numerical range and their connections with eigenvalues are described.


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Additional Information

Chi-Kwong Li
Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187
Email: ckli@math.wm.edu

Leiba Rodman
Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187
Email: lxrodm@math.wm.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04242-7
PII: S 0002-9939(98)04242-7
Keywords: Numerical range, indefinite scalar product, Krein space.
Received by editor(s): September 23, 1996
Additional Notes: Research of both authors was partially supported by NSF Grants.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society