On a J-Polar Decomposition of a Bounded Operator and Matrices of J-Symmetric and J-Skew-Symmetric Operators (Report‪)‬

1. INTRODUCTION AND PRELIMINARIES Complex symmetric, skew-symmetric and orthogonal matrices are classical objects of the finite-dimensional linear analysis [4]. In particular, the normal forms are known for them, see [4, Chapter XI]. Certainly, they have more complicated structures as for Hermitian matrices. However, in a certain sense complex symmetric matrices are more universal. Namely, an arbitrary square complex matrix is similar to a symmetric matrix [4, Chapter XI, p.321]. A generalization of complex symmetric, skew-symmetric and orthogonal matrices leads to the well-known J-symmetric, J-skew-symmetric and J-isometric operators.