Factorization of Operators in Krein Spaces and Linear-Fractional Relations of Operator Balls

Victor Anatoly Khatskevich, Valery Anatoly Senderov

Department of Mathematics, ORT Braude Academic College, Karmiel, Israel.
Pyatnitskoe Highway, 23-2-156, Moscow, Russia.

DOI: 10.4236/apm.2013.31006                

Abstract

We consider plus-operators in Krein spaces and generated operator linear fractional relations of the following form:

.

We study some special type of factorization for plus-operators T, among them the following one: T = BU, where B is a lower triangular plus-operator, U is a J-unitary operator. We apply the above factorization to the study of basical properties of relations (1), in particular, convexity and compactness of their images with respect to the weak operator topology. Obtained results we apply to the known Koenigs embedding problem, the Krein-Phillips problem of existing of invariant semidefinite subspaces for some families of plus-operators and to some other fields.

Keywords

Krein Space; Linear Fractional Relation; Plus-Operator; Factorization

Conflicts of Interest

The authors declare no conflicts of interest.

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