an: Zbl 1200.47050
au: Zagorodnyuk, Sergey M.
ti: On a $J$-polar decomposition of a bounded operator and matrices of
    $J$-symmetric and $J$-skew-symmetric operators.
la: EN
so: Banach J. Math. Anal. 4, No. 2, 11-36, electronic only (2010).
py: 2010
dt: J
cc: *47B99 15B99
ut: $J$-symmetric operator; $J$-skew-symmetric operator; polar decomposition;
    matrix of an operator
ab: 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.
rv: Anatoly N. Kochubei (Ky\"\i v)