Invariant Maximal Positive Subspaces and Polar Decompositions
It is proved that invertible operators on a Krein space which have an invariant maximal uniformly positive subspace and map its orthogonal complement into a nonnegative subspace allow polar decompositions with additional spectral properties. As a corollary, several classes of Krein space operators are shown to allow polar decompositions. An example in a finite dimensional Krein space shows that there exist dissipative operators that do not allow polar decompositions.
Mathematics Subject Classification (2000).Primary 47B44 46C20
Keywords.Krein space invariant subspace dissipative operator polar decomposition
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