scholarly journals Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces

1998 ◽  
Vol 131 (3) ◽  
pp. 289-302 ◽  
Author(s):  
G. Krupa
Keyword(s):  
Banach Spaces ◽  
Random Sets ◽  
Ergodic Theorems

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.

Modulated and subsequential ergodic theorems in Hilbert and Banach spaces

2002 ◽  
Vol 22 (06) ◽  
Author(s):  
D. BEREND ◽  
M. LIN ◽  
J. ROSENBLATT ◽  
A. TEMPELMAN
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorems

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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