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On a J-polar decomposition of a bounded operator and matrices of J-symmetric and J-skew-symmetric operators. (English) Zbl 1200.47050
The author considers the classes of J-symmetric operators and J-selfadjoint operators on a Hilbert space with respect to an antilinear involution J, as well as various related classes. These classes should not be confused with the similar classes of operators on a Krein or Pontryagin space. Some specific features of matrix representations of J-symmetric and J-skew-symmetric operators are studied. The main result of the paper provides conditions under which a bounded linear operator can be represented as a product of a J-unitary operator and a J-selfadjount one. A good bibliography concerning operators on spaces with an antilinear involution is given.
MSC:
47B99Special classes of linear operators
15B99Special matrices