On contractions in Hilbert space

Abstract

In the first part of the paper we study the decompositions of a (bounded linear) operator similar to a normal operator in Hilbert space into the orthogonal of a normal (self-adjoint, unitary) part and of a part free of the given property, respectively. In the second part we investigate in a finite dimensional Hilbert space the minimal unitary power dilations (till the exponent k) of a contraction. We determine the general form of ch dilations, examine their spectra, and the question of their isomorphy. The first step of the study here is also the decomposition of the contraction into unitary and completely non-unitary parts.