scholarly journals A volume-based approach to the multiplicative ergodic theorem on Banach spaces

2015 ◽  
Vol 36 (5) ◽  
pp. 2377-2403 ◽  
Author(s):  
Alex Blumenthal
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Multiplicative Ergodic Theorem

scholarly journals A concise proof of the multiplicative ergodic theorem on Banach spaces

2015 ◽  
Vol 9 (01) ◽  
pp. 237-255 ◽  
Author(s):  
Cecilia González-Tokman ◽  
◽  
Anthony Quas ◽  
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Multiplicative Ergodic Theorem

ON THE ABSOLUTE REGULARITY OF LINEAR RANDOM DYNAMICAL SYSTEMS

2003 ◽  
Vol 03 (04) ◽  
pp. 453-461 ◽  
Author(s):  
LUU HOANG DUC
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theorem ◽  
Random Dynamical Systems ◽  
Absolute Regularity ◽  
Integrability Conditions ◽  
Multiplicative Ergodic Theorem ◽  
Lyapunov Regularity ◽  
The Absolute

We introduce a concept of absolute regularity of linear random dynamical systems (RDS) that is stronger than Lyapunov regularity. We prove that a linear RDS that satisfies the integrability conditions of the multiplicative ergodic theorem of Oseledets is not merely Lyapunov regular but absolutely regular.

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.

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