scholarly journals On The Strong Ergodic Theorems for Commutative Semigroups in Banach Spaces

1993 ◽  
Vol 16 (2) ◽  
pp. 385-398 ◽  
Author(s):  
Hirokazu OKA
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorems ◽  
Commutative Semigroups

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
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