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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 88, Issue 1
  • July 1980, pp. 135-147

Ergodic theorems for semifinite von Neumann algebras: II

  • F. J. Yeadon (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100057418
  • Published online: 24 October 2008
Abstract

In (7) we proved maximal and pointwise ergodic theorems for transformations a of a von Neumann algebra which are linear positive and norm-reducing for both the operator norm ‖ ‖ and the integral norm ‖ ‖1 associated with a normal trace ρ on . Here we introduce a class of Banach spaces of unbounded operators, including the Lp spaces defined in (6), in which the transformations α reduce the norm, and in which the mean ergodic theorem holds; that is the averages

converge in norm.

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(3)I. E. Segal A non-commutative extension of abstract integration. Ann of Math. 57 (1952), 401457.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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