Abstract.
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.
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Mehl, C., Ran, A.C.M. & Rodman, L. Invariant Maximal Positive Subspaces and Polar Decompositions. Integr. equ. oper. theory 56, 83–91 (2006). https://doi.org/10.1007/s00020-005-1407-z
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DOI: https://doi.org/10.1007/s00020-005-1407-z