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The Numerical Range of 2-Dimensional Krein Space Operators

Published online by Cambridge University Press:  20 November 2018

Hiroshi Nakazato ,
Natália Bebiano  and
João da Providência
Hiroshi Nakazato
Affiliation:
Department of Mathematical Sciences, Hirosaki University, 036-8561 Hirosaki, Japan e-mail: nakahr@cc.hirosaki-u.ac.jp
Natália Bebiano
Affiliation:
Mathematics Department, University of Coimbra, P 3000 Coimbra, Portugal e-mail: bebiano@mat.uc.pt
João da Providência
Affiliation:
Physics Department, University of Coimbra, P 3000 Coimbra, Portugal e-mail: providencia@teor.fis.uc.pt
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Abstract

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The tracial numerical range of operators on a 2-dimensional Krein space is investigated. Results in the vein of those obtained in the context of Hilbert spaces are obtained.

Keywords

15A6015A6315A45numerical rangegeneralized numerical rangeindefinite inner product space
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 1 , 01 March 2008 , pp. 86 - 99
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Bebiano, N., Lemos, R., da Providência, J., and Soares, G., On the geometry of numerical ranges in spaces with an indefinite inner product. Linear Algebra Appl. 399(2005), 17–34.Google Scholar
[2] Bebiano, N., Nakazato, H., da Providência, J., Lemos, R., and Soares, G., Inequalities for J-Hermitian matrices. Linear Algebra Appl. 407(2005), 125–139.Google Scholar
[3] Helgason, S., Differential Geometry, Lie Groups, and Symmetric Spaces. Pure and Applied Mathematics 80, Academic Press, New York, 1978.Google Scholar
[4] Li, C.-K. and Rodman, L., Remarks on numerical ranges of operators in spaces with an indefinite metric. Proc. Amer.Math. Soc. 126(1998), no. 4, 973–982.Google Scholar
[5] Li, C.-K., Tsing, N. K., and Uhlig, F., Numerical ranges of an operator on an indefinite inner product space. Electron. J. Linear Algebra 1(1996), 1–17.Google Scholar
[6] Psarrakos, P., Numerical range of linear pencils. Linear Algebra Appl. 317(2000), no. 1–3, 127–141.Google Scholar