Zagorodnyuk, Sergey M. On a \(J\)-polar decomposition of a bounded operator and matrices of \(J\)-symmetric and \(J\)-skew-symmetric operators. (English) Zbl 1200.47050 Banach J. Math. Anal. 4, No. 2, 11-36 (2010). 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. Reviewer: Anatoly N. Kochubei (Kyïv) Cited in 19 Documents MSC: 47B99 Special classes of linear operators 15B99 Special matrices Keywords:\(J\)-symmetric operator; \(J\)-skew-symmetric operator; polar decomposition; matrix of an operator × Cite Format Result Cite Review PDF Full Text: DOI arXiv EuDML EMIS