  In this work a possibility of a decomposition of a bounded operator which
acts in a Hilbert space $H$ as a product of a J-unitary and a J-self-adjoint
operators is studied, $J$ is a conjugation (an antilinear involution).
Decompositions of J-unitary and unitary operators which are analogous to
decompositions in the finite-dimensional case are obtained. A possibility of a
matrix representation for J-symmetric, J-skew-symmetric operators is studied.
Also, some simple properties of J-symmetric, J-antisymmetric, J-isometric
operators are obtained, a structure of a null set for a J-form is studied.
