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Archiv der Mathematik

, Volume 72, Issue 3, pp 214–218 | Cite as

Mean ergodicity on Banach lattices and Banach spaces

  • Eduard Yu. Emel’yanov
  • Manfred P.H. Wolff
Article

Abstract.

We characterize properties of Banach spaces by mean ergodicity of operators belonging to special classes. More precisely, we prove: ¶ (i) The Banach lattice E has order continuous norm iff every power-order-bounded regular Fredholm operator is ergodic. (ii) The countably order complete Banach lattice is a KB-space iff every positive operator which possesses a quasi order bounded attractor is mean ergodic. (iii) The Banach space does not contain c0 if every Fredholm operator is ergodic.

Keywords

Banach Space Special Classis Positive Operator Banach Lattice Fredholm Operator 

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Eduard Yu. Emel’yanov
    • 1
  • Manfred P.H. Wolff
    • 2
  1. 1.Sobolev Institute of Mathematics at Novosibirsk, Universitetskii pr. 4, RU-630090, Novosibirsk, RussiaRussia
  2. 2.Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 2, D-720776 Tübingen, GermanyDeutschland

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