Wu, Jingbo Normal extensions of semigroups of operators to Krein spaces. (English) Zbl 0767.47023 Acta Math. Sin., New Ser. 7, No. 3, 205-215 (1991). 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.) Keywords:strongly continuous semigroup of bounded operators on a Hilbert space semigroup of normal operators on a Krein space; extension space; Pontrjagin space PDFBibTeX XMLCite \textit{J. Wu}, Acta Math. Sin., New Ser. 7, No. 3, 205--215 (1991; Zbl 0767.47023) Full Text: DOI References: [1] Bognár, J., Indefinite inner product spaces, Springer-Verlag, Berlin-Heidelberg, 1974. [2] Hille, E. and Phillips, R. S., Functional analysis and semi-groups,Amer. Math. Soc. Colloq. Publ.,31 (1957). · Zbl 0078.10004 [3] Iohvidov, I. S., Krein, M. G. and Langer, H., Introduction to the spectral theory of operators in spaces with an indefinite metric. Akademie-Verlag, Berlin, 1982. · Zbl 0506.47022 [4] Itô, T., On the commutative family of subnormal operators,J. Fac. Sci. Hokkaido Univ.,14 (1958), 1–15. · Zbl 0089.32302 [5] Kato, T., Perturbation theory for linear operators, Springer-Verlag, New York, 1966. · Zbl 0148.12601 [6] Wu Jingbo, On theJ-normal extension of operators,Chin. Ann. Math.,3 (1982), 609–616 (in Chinese). · Zbl 0504.47027 [7] Wu Jingbo, Normal extensions of operators to Krein spaces,Chin. Ann. Math.,8B (1987), 36–42. · Zbl 0641.47043 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.