×

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:

47B99 Special classes of linear operators
15B99 Special matrices