<i>H</i>-joint numerical ranges

Li, Chi-Kwong; Rodman, Leiba

doi:10.1017/s0004972700020724

Bull. Austral. Math. Soc.

2002

DOI: 10.1017/s0004972700020724

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H-joint numerical ranges

Chi-Kwong Li¹,

Leiba Rodman²

Abstract: The notion of the joint numerical range of several linear operators with respect to a sesquilinear form is introduced. Geometrical properties of the joint numerical range are studied, in particular, convexity and angle points, in connection with the algebraic properties of the operators. The main focus is on the finite dimensional case.

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Cited by 2 publications

References 14 publications

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Shells of matrices in indefinite inner product spaces

Bolotnikov¹,

Li²,

Meade³

et al. 2002

ELA

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Abstract. The notion of the shell of a Hilbert space operator, which is a useful generalization (proposed by Wielandt) of the numerical range, is extended to operators in spaces with an indefinite inner product. For the most part, finite dimensional spaces are considered. Geometric properties of shells (convexity, boundedness, being a subset of a line, etc.) are described, as well as shells of operators in two dimensional indefinite inner product spaces. For normal operators, it is conjectured that the shell is convex and its closure is polyhedral; the conjecture is proved for indefinite inner product spaces of dimension at most three, and for finite dimensional inner product spaces with one positive eigenvalue.

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Shells of matrices in indefinite inner product spaces

Bolotnikov¹,

Li²,

Meade³

et al. 2002

ELA

Self Cite

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A note on the convexity of the indefinite joint numerical range

Nakazato

Bebiano

Providência

2014

ELA

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H-joint numerical ranges

Cited by 2 publications

References 14 publications

Shells of matrices in indefinite inner product spaces

Shells of matrices in indefinite inner product spaces

A note on the convexity of the indefinite joint numerical range

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