Decompositions of a Krein space in regular subspaces invariant under a uniformly bounded C0-semigroup of bi-contractions |
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| Authors: | TYa Azizov |
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| Institution: | a Department of Mathematics, Voronezh State University, Universitetskaya pl. 1, Voronezh 394693, Russia
b Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands |
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| Abstract: | We give necessary and sufficient conditions under which a C0-semigroup of bi-contractions on a Krein space is similar to a semigroup of contractions on a Hilbert space. Under these and additional conditions we obtain direct sum decompositions of the Krein space into invariant regular subspaces and we describe the behavior of the semigroup on each of these summands. In the last section we give sufficient conditions for the co-generator of the semigroup to be power bounded. |
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| Keywords: | primary 47D60 47B50 secondary 47A20 47A15 |
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