Remarks on numerical ranges of operators in spaces with an indefinite metric
HTML articles powered by AMS MathViewer
- by Chi-Kwong Li and Leiba Rodman PDF
- Proc. Amer. Math. Soc. 126 (1998), 973-982 Request permission
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
- Yik Hoi Au-Yeung and Nam-Kiu Tsing, An extension of the Hausdorff-Toeplitz theorem on the numerical range, Proc. Amer. Math. Soc. 89 (1983), no. 2, 215–218. MR 712625, DOI 10.1090/S0002-9939-1983-0712625-4
- T. Ya. Azizov and I. S. Iokhvidov, Linear operators in spaces with an indefinite metric, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1989. Translated from the Russian by E. R. Dawson; A Wiley-Interscience Publication. MR 1033489
- Ts. Bayasgalan, The numerical range of linear operators in spaces with an indefinite metric, Acta Math. Hungar. 57 (1991), no. 1-2, 7–9 (Russian). MR 1128834, DOI 10.1007/BF01903796
- Paul Binding and Chi-Kwong Li, Joint ranges of Hermitian matrices and simultaneous diagonalization, Linear Algebra Appl. 151 (1991), 157–167. MR 1102147, DOI 10.1016/0024-3795(91)90361-Y
- R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. MR 203464, DOI 10.1090/S0002-9939-1966-0203464-1
- I. M. Glazman and Yu. I. Lyubich, Konechnomernyĭ lineĭnyĭ analiz v zadachakh, Izdat. “Nauka”, Moscow, 1969 (Russian). MR 0354715
- I. Gohberg, P. Lancaster, and L. Rodman, Matrices and indefinite scalar products, Operator Theory: Advances and Applications, vol. 8, Birkhäuser Verlag, Basel, 1983. MR 859708
- R. D. Grigorieff and R. Plato, On a minimax equality for seminorms, Linear Algebra Appl. 221 (1995), 227–243. MR 1331802, DOI 10.1016/0024-3795(93)00258-2
- Roger A. Horn and Charles R. Johnson, Topics in matrix analysis, Cambridge University Press, Cambridge, 1991. MR 1091716, DOI 10.1017/CBO9780511840371
- Chi-Kwong Li, Nam-Kiu Tsing, and Frank Uhlig, Numerical ranges of an operator on an indefinite inner product space, Electron. J. Linear Algebra 1 (1996), 1–17. MR 1401906, DOI 10.13001/1081-3810.1000
- C.K. Sze, S-normality and polygonal S-numerical ranges, M. Phil. Thesis, University of Hong Kong, 1997.
Additional Information
- Chi-Kwong Li
- Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187
- MR Author ID: 214513
- 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
- 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 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 973-982
- MSC (1991): Primary 15A60, 47A12, 47A37
- DOI: https://doi.org/10.1090/S0002-9939-98-04242-7
- MathSciNet review: 1443838