Geodesic
Shapes and computer generation of numerical ranges of Krein space operators
The electronic journal of linear algebra, Tome 3 (1998), pp. 31-47.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $({\cal K},\langle\cdot, \cdot\rangle)$ be a Hilbert space equipped with an indefinite inner product $[\cdot,\cdot]$. Then $({\cal K},[\cdot, \cdot])$ is a (complex) Krein space. One can define the Krein space numerical range of an operator $A$ acting on ${\cal K}$ as the collection of complex numbers of the form $[Av,v]$ with $v\in{\cal K}$ satisfying $[v, v]= 1$. In this paper, the shapes of Krein space numerical ranges of operators in the complex plane using the joint numerical range of selfadjoint operators on $({\cal K},\langle\cdot, \cdot\rangle)$ are studied. Krein space numerical ranges of operators acting on a two-dimensional space are fully described. A Matlab program is developed to generate the sets in the finite-dimensional case.
Classification : 15A60, 15A63
Keywords: indefinite inner product, krein space, numerical range AMS subject 
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     author = {Li, Chi-Kwong and Rodman, Leiba},
     title = {Shapes and computer generation of numerical ranges of {Krein} space operators},
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     publisher = {mathdoc},
     volume = {3},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_1998__3__a7/}
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Li, Chi-Kwong; Rodman, Leiba. Shapes and computer generation of numerical ranges of Krein space operators. The electronic journal of linear algebra, Tome 3 (1998), pp. 31-47. http://geodesic.mathdoc.fr/item/ELA_1998__3__a7/