The author considers the classes of
-symmetric operators and
-selfadjoint operators on a Hilbert space with respect to an antilinear involution
, 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
-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
-unitary operator and a
-selfadjount one. A good bibliography concerning operators on spaces with an antilinear involution is given.