Fixed Point Properties of Amenable Semigroups and Nonlinear Ergodic Theorems

• Andrzej Wisnicki ^[1]
  1. [1] University of Life Sciences

     University of Life Sciences

     Lublin, Polonia

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 2, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We characterize amenability of subspaces of C(S), where S is a semigroup, in terms of fixed point properties of nonexpansive (1-Lipschitz) actions. In particular, using the notion of fragmentability, we give a complete characterization of semitopological semigroups with a left invariant mean on the spaceWAP(S) of weakly almost periodic functions on S that answers a question of [A.T.-M. Lau, Y. Zhang, J. Funct. Anal.

    263 (2012), 2949–2977] in the affirmative. We also use Bruck’s method to show the existence of nonexpansive retractions onto common fixed point sets of S-actions and apply a fixed point theorem for semigroups with a LIM onWAP(S) to obtain nonlinear ergodic theorems in the spirit of [A.T.-M. Lau, N. Shioji,W. Takahashi, J. Funct. Anal.

    161 (1999), 62–75].

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