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Quadratic cones invariant under some linear operators. (English) Zbl 0619.15022

A quadratic cone in a finite dimensional space is the set of x satisfying f(x,x)\(\geq 0\), where f in an indefinite Hermitian form. The author characterizes the linear operators which have such a fixed cone invariant. He shows furthermore that if the spectral radius and the norm of an operator A coincide for a submultiplicative norm on the operators then there exists an A-invariant quadratic cone of specified signature.
Reviewer: T.B.Andersen

MSC:

15A63 Quadratic and bilinear forms, inner products
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15A18 Eigenvalues, singular values, and eigenvectors
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