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Normal extensions of semigroups of operators to Krein spaces. (English) Zbl 0767.47023

Summary: We prove that every strongly continuous semigroup of bounded operators on a Hilbert space may be extended to a strongly continuous semigroup of normal operators on a larger Kreĭn space. Several equivalent formulations for the case where the extension space is a Pontrjagin space are given.

MSC:

47D06 One-parameter semigroups and linear evolution equations
47B50 Linear operators on spaces with an indefinite metric
46C20 Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.)
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References:

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