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Zbl 1200.47050
Zagorodnyuk, Sergey M.
On a $J$-polar decomposition of a bounded operator and matrices of $J$-symmetric and $J$-skew-symmetric operators. (English)
[J] Banach J. Math. Anal. 4, No. 2, 11-36, electronic only (2010). ISSN 1735-8787/e

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.
[Anatoly N. Kochubei (Ky\"iv)]

MSC 2000:: *47B99 Special classes of linear operators
15B99

Keywords: $J$-symmetric operator; $J$-skew-symmetric operator; polar decomposition; matrix of an operator

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