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Ergodic conditions and spectral properties for A-contractions

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In this paper the canonical representation of an A-contraction T on a Hilbert space H is used to obtain some conditions concerning the concept of A-ergodicity studied in [14-17]. The regular case and the case of 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.
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195--216
Opis fizyczny
Bibliogr. 19 poz.
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Bibliografia
  • [1] P.L. Butzer, U. Westphal, The Mean Ergodic Theorem and Saturation, Indiana University Mathematical Journal, 20 (1971) 12, 1163–1174.
  • [2] G. Cassier, L. Suciu, Mapping theorems and similarity to contractions for classes of A-contractions, Operator Theory: Advances and Applications, Proceedings of 21th Conference on Operator Theory, Timisoara, 2006, 1–25 [to appear].
  • [3] R.G. Douglas, On majorization, factorization and range inclusion of operators in Hilbert space, Proc. Amer. Math. Soc., 17 (1966), 413–416.
  • [4] R.G. Douglas, On the operator equation S*XT = X and related topics, Acta. Sci. Math. (Szeged), 30 (1969), 19–32.
  • [5] T. Furuta, Invitation to Linear Operators. From matrices to bounded linear operators on Hilbert space, Taylor-Francis, 2001, 255.
  • [6] C.S. Kubrusly, An introduction to Models and Decompositions in Operator Theory. Birkhäuser, Boston, 1997.
  • [7] C.S. Kubrusly, Hilbert Space Operators. A Problem Solving Approach. Birkhäuser, Boston, 2003.
  • [8] W. Mlak, Hyponormal contractions, Coll. Math., 18 (1967), 137–142.
  • [9] M. Mbekhta, L. Suciu, Classes of operators similar to partial isometries, Preprint, 1–22.
  • [10] S. Miyajima, I. Saito, 1-hyponormal operators and their spectral properties. Acta Sci. Math. (Szeged), 67 (2001), 357–371.
  • [11] S.M. Patel, A note on quasi-isometries, Glasnik Matematicki, 35 (2000) 55, 307–312.
  • [12] S.M. Patel, A note on quasi-isometries II, Glasnik Matematicki, 38 (2003) 58, 111–120.
  • [13] J.G. Stampfli, Hyponormal operators, Pacific J. Math., 12 (1962), 1453–1458.
  • [14] L. Suciu, Orthogonal decompositions induced by generalized contractions, Acta Sci. Math. (Szeged), 70 (2004), 751–765.
  • [15] L. Suciu, On the ergodic A-contractions, Analele Universitaµii de Vest din Timisoara, Ser. Mat.-Inf., 2 (2004), 115–136.
  • [16] L. Suciu, Ergodic properties for regular A-contractions, Integral Equations and Operator Theory, 56 (2006) 2, 285–299.
  • [17] L. Suciu, Ergodic properties and saturation for A-contractions, Operator Theory: Advances and Applications; Proceeding of 20th Conference on Operator Theory, Timisoara 2004, Theta 2006, 225–242.
  • [18] L. Suciu, Some invariant subspaces for A-contractions and applications, Extracta Mathematicae, 21 (2006) 3, 221–247.
  • [19] Y. Tomilov, J. Zemànek, A new way of constructing examples in operator ergodic theory, Math. Proc. Camb. Philos. Soc., 137 (2004) 9.1, 209–225.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHB-0001-0008
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