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Remarks on numerical ranges of operators in spaces with an indefinite metric
Author(s):
Chi-Kwong
Li;
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.
References:
- [AT]
- Y.H. Au-Yeung and N.K. Tsing, An extension of the Hausdorff-Toeplitz theorem on the numerical range, Proc. Amer. Math. Soc. 89 (1983), 215-218. MR 85f:15021
- [AI]
- T. Ya. Azizov and I. Iohvidov, Linear Operators in Spaces with Indefinite Metric, J. Wiley and Sons, 1989, (Translation from Russian). MR 90j:47042
- [B]
- T. Bayasgalan, The numerical range of linear operators in spaces with an indefinite metric (Russian), Acta Math. Hungar. 57 (1991), 7-9. MR 93a:47036
- [BL]
- P. Binding and C.K. Li, Joint ranges of Hermitian matrices and simultaneous diagonalization, Linear Algebra Appl. 151 (1991), 157-168. MR 92d:47006
- [D]
- R.G. Douglas, On majorization, factorization, and range inclusion of operators in Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413-415. MR 34:3315
- [GL]
- I.M. Glazman and Yu. I. Lyubich, Finite Dimensional Linear Analysis, Nauka, Moscow, 1969 (in Russian; English transl., M.I.T. Press, Cambridge, MA, 1974). MR 50:7192; MR 50:7195
- [GLR]
- I. Gohberg, P. Lancaster and L. Rodman, Matrices and Indefinite Scalar Products, Birkhäuser, 1983. MR 87j:15001
- [GP]
- R.D. Grigorieff and R. Plato, On the minimax equality for seminorms, Linear Algebra Appl. 221 (1995), 227-243. MR 96e:15049
- [HJ]
- R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991. MR 92e:15003
- [LTU]
- C.K.Li, N.K.Tsing and F. Uhlig, Numerical ranges of an operator on an indefinite inner product space, Electronic Linear Algebra 1 (1996), 1-17. MR 97g:47005
- [S]
- C.K. Sze, S-normality and polygonal S-numerical ranges, M. Phil. Thesis, University of Hong Kong, 1997.
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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