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2000 | 86 | 2 | 163-170
Tytuł artykułu

On unrestricted products of (W) contractions

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a family of (W) contractions $T_1, ..., T_N$ on a reflexive Banach space X we discuss unrestricted sequences $T_{r_n}∘...∘T_{r_1}(x)$. We show that they converge weakly to a common fixed point, which depends only on x and not on the order of the operators $T_{r_n}$ if and only if the weak operator closed semigroups generated by $T_1, ..., T_N$ are right amenable.
Rocznik
Tom
86
Numer
2
Strony
163-170
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-11-24
poprawiono
1999-11-16
Twórcy
  • Department of Mathematics, University of South Africa, P.O. Box 392, 0003 Pretoria, South Africa
Bibliografia
  • [AA] I. Amemiya and T. Ando, Convergence of random products of contractions in Hilbert space, Acta Sci. Math. (Szeged) 26 (1965), 239-244.
  • [B] R. E. Bruck, Random products of contractions in metric and Banach spaces, J. Math. Anal. Appl. 88 (1982), 319-332.
  • [BA] H. H. Bauschke, A norm convergence result of random products of relaxed projections in Hilbert space, Trans. Amer. Math. Soc. 347 (1995), 1365-1373.
  • [DKLR] J. M. Dye, T. Kuczumow, P.-K. Lin and S. Reich, Convergence on unrestricted products of nonexpansive mappings in spaces with the Opial property, Nonlinear Anal. 26 (1996), 767-773.
  • [DLG] K. DeLeeuw and I. Glickberg, Applications of almost periodic compactifications, Acta Math. 105 (1961), 63-97.
  • [D] J. Dye, A generalization of a theorem of Amemiya and Ando on the convergence of random products of contractions in Hilbert space, Integral Equations Oper. Theory 12 (1989), 155-162.
  • [DKR] J. Dye, M. A. Khamsi and S. Reich, Random products of contractions in Banach spaces, Trans. Amer. Math. Soc. 325 (1991), 87-99.
  • [DR] J. M. Dye and S. Reich, On the unrestricted iteration of projections in Hilbert space, J. Math. Anal. Appl. 156 (1991), 101-119.
  • [L] P.-K. Lin, Unrestricted products of contractions in Banach spaces, Nonlinear Anal. 24 (1995), 1103-1108.
  • [N] J. von Neumann, On rings of operators. Reduction theory, Ann. of Math. 44 (1943), 401-485.
  • [R] S. Reich, The alternating algorithm of von Neumann in the Hilbert ball, Dynamic Systems Appl. 2 (1993), 21-26.
  • [RZ] S. Reich and A. J. Zaslavski, Convergence of generic infinite products of order-preserving mappings, Positivity 3 (1999), 1-21.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv86i2p163bwm
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