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Extension to maximal semidefinite invariant subspaces for hyponormal matrices in indefinite inner products |
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| Authors: | Christian Mehl,André C.M. Ran |
| Affiliation: | a Fakultät II, Institut für Mathematik, Technische Universität Berlin, D-10623 Berlin, Germany b Afdeling Wiskunde, Faculteit der Exacte Wetenschappen, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands c College of William and Mary, Department of Mathematics, P.O. Box 8795, Williamsburg, VA 23187-8795, United States |
| Abstract: | It is proved that under certain essential additional hypotheses, a nonpositive invariant subspace of a hyponormal matrix admits an extension to a maximal nonpositive subspace which is invariant for both the matrix and its adjoint. Nonpositivity of subspaces and the hyponormal property of the matrix are understood in the sense of a nondegenerate inner product in a finite dimensional complex vector space. The obtained theorem combines and extends several previously known results. A Pontryagin space formulation, with essentially the same proof, is offered as well. |
| Keywords: | 15A63 15A57 |
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