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ELA

THE NUMERICAL RANGE OF LINEAR OPERATORS

ON THE 2-DIMENTIONAL KREIN SPACE

∗

HIROSHI NAKAZATO†, NAT ´ALIA BEBIANO‡, AND JO ˜AO DA PROVIDˆENCIA§

Abstract. The aim of this note is to provide the complete characterization of the numerical range of linear operators on the 2-dimensional Krein spaceC2.

Key words. Krein space, Numerical range, Rank one operator.

AMS subject classifications. 46C20, 47A12.

∗Received by the editors on November 22, 2010. Accepted for publication on April 2, 2011.

Handling Editor: Michael Tsatsomeros.

†Department of Mathematical Sciences, Hirosaki University, 036-8561, Japan

([email protected]).

‡Mathematics Department, University of Coimbra, P3001-454 Coimbra, Portgal

([email protected]).

§Physics Department, University of Coimbra, P3004-516 Coimbra, Portgal

([email protected]).

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 22, pp. 430-442, April 2011

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