scholarly journals An abstract ergodic theorem and some inequalities for operators on Banach spaces

1997 ◽  
Vol 125 (1) ◽  
pp. 111-119 ◽  
Author(s):  
Yuan-Chuan Li ◽  
Sen-Yen Shaw
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Inequalities For Operators

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.

A Pointwise Ergodic Theorem in Lp-Spaces

1975 ◽  
Vol 27 (5) ◽  
pp. 1075-1082 ◽  
Author(s):  
M. A. Akcoglu
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Ergodic Theorem ◽  
Measure Space ◽  
Positive Contraction ◽  
Lp Spaces ◽  
Pointwise Ergodic Theorem ◽  
Image Position

Let be a measure space and the usual Banach spaces. A linear operator T : Lp → Lpis called a positive contraction if it transforms non-negative functions into non-negative functions and if its norm is not more than one. The purpose of this note is to show that if 1 < p < ∞ and if T : Lp → Lp is a positive contraction then

scholarly journals Linear Sequences and Weighted Ergodic Theorems

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Tanja Eisner
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Return Time ◽  
Linear Operators ◽  
Full Measure ◽  
Ergodic Theorems ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Time Sequences

We present a simple way to produce good weights for several types of ergodic theorem including the Wiener-Wintner type multiple return time theorem and the multiple polynomial ergodic theorem. These weights are deterministic and come from orbits of certain bounded linear operators on Banach spaces. This extends the known results for nilsequences and return time sequences of the form for a measure preserving system and , avoiding in the latter case the problem of finding the full measure set of appropriate points .

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