Ergodic conditions and spectral properties for A-contractions

In this paper the canonical representation of an \(A\)-contraction \(T\) on a Hilbert space \(\mathcal{H}\) is used to obtain some conditions concerning the concept of \(A\)-ergodicity studied in [L. Suciu, Orthogonal decompositions induced by generalized contractions, Acta Sci. Math. (Szeged) 70 (2004), 751–765; L. Suciu, On the ergodic \(A\)-contractions, Analele Universitaţii de Vest din Timişoara, Ser. Mat.-Inf. 2 (2004), 115–136; L. Suciu, Ergodic properties for regular \(A\)-contractions, Integral Equations and Operator Theory 56 (2006) 2, 285–299; L. Suciu, Ergodic properties and saturation for \(A\)-contractions, Operator Theory: Advances and Applications; Proceeding of 20th Conference on Operator Theory, Timişoara 2004, Theta 2006, 225–242]. The regular case and the case of \(\mathcal{R}(A)\) closed are considered, and specifically, the \(TT^{*}\)-contractions are studied. Some spectral properties are also given for certain particular class of \(A\)-isometries.