Skip to main content
×
Home
    • Aa
    • Aa

Ergodic theorems for semifinite von Neumann algebras: II

  • F. J. Yeadon (a1)
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.

Copyright
References
Hide All
(1)Fremlin D. H. Stable subspaces of L 1 + L . Proc. Cambridge Philos. Soc. 64 (1968), 625643.
(2)Luxemburg W. A. J. and Zaanen A. C. Notes on Banach function spaces. I-IV; XIII. Nederl. Akad. Wetensch. 66 (A) (1963); 67 (A) (1964).
(3)Segal I. E. A non-commutative extension of abstract integration. Ann of Math. 57 (1952), 401457.
(4)Yeadon F. J. Modules of measurable operators. Dissertation, Cambridge, 1968.
(5)Yeadon F. J. Convergence of measurable operators, Proc. Cambridge Philos. Soc. 74 (1973), 257268.
(6)Yeadon F. J. Non-commutative -L-spaces, Proc. Cambridge Philos. Soc. 77 (1975), 91102.
(7)Yeadon F. J. Ergodic theorems for semifinite von Neumann algebras: I. J. London Math. Soc. (2) 16 (1977), 326332.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 13 *
Loading metrics...

Abstract views

Total abstract views: 69 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd October 2017. This data will be updated every 24 hours.