Opuscula Math. 28, no. 2 (2008), 195-216

Opuscula Mathematica

# Ergodic conditions and spectral properties for A-contractions

Laurian Suciu
Nicolae Suciu

Abstract. 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.

Keywords: mean ergodic operator, $$A$$-contraction, isometry, spectrum.

Mathematics Subject Classification: 47A35, 47A62, 47A65, 47A63, 47B20.

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• Laurian Suciu
• University Claude Bernard Lyon 1, Institut Camille Jordan, 69622 Villeurbanne Cedex, France
• Nicolae Suciu
• West University of Timişoara, Department of Mathematics, Bv. V. Parvan 4, Timişoara 300223, Romania