A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces

1979 ◽  
Vol 32 (2-3) ◽  
pp. 107-116 ◽  
Author(s):  
Ronald E. Bruck
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Simple Proof ◽  
Mean Ergodic Theorem ◽  
The Mean ◽  
Nonlinear Contractions

scholarly journals A quantitative mean ergodic theorem for uniformly convex Banach spaces

2009 ◽  
Vol 29 (6) ◽  
pp. 1907-1915 ◽  
Author(s):  
U. KOHLENBACH ◽  
L. LEUŞTEAN
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Hilbert Spaces ◽  
Local Stability ◽  
Uniformly Convex ◽  
Norm Convergence ◽  
Ergodic Averages ◽  
Mean Ergodic Theorem ◽  
Uniformly Convex Banach Spaces ◽  
The Mean

AbstractWe provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of Tao of the mean ergodic theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad et al [Local stability of ergodic averages. Trans. Amer. Math. Soc. to appear] and Tao [Norm convergence of multiple ergodic averages for commuting transformations. Ergod. Th. & Dynam. Sys.28(2) (2008), 657–688].

Ergodic theorems for semifinite von Neumann algebras: II

1980 ◽  
Vol 88 (1) ◽  
pp. 135-147 ◽  
Author(s):  
F. J. Yeadon
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Operator Norm ◽  
Ergodic Theorems ◽  
Unbounded Operators ◽  
Von Neumann ◽  
The Mean ◽  
Image Position

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 averagesconverge in norm.

Uniform distribution and the mean ergodic theorem

1978 ◽  
Vol 50 (1) ◽  
pp. 65-74 ◽  
Author(s):  
V. Losert ◽  
H. Rindler
Keyword(s):  
Uniform Distribution ◽  
Ergodic Theorem ◽  
Mean Ergodic Theorem ◽  
The Mean
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