scholarly journals Ergodic theorems for semigroups of operators on a Grothendieck space

1983 ◽  
Vol 59 (4) ◽  
pp. 132-135 ◽  
Author(s):  
Sen-Yen Shaw
Keyword(s):  
Semigroups Of Operators ◽  
Ergodic Theorems ◽  
Grothendieck Space

Some ergodic theorems for one-parameter semigroups of operators

1956 ◽  
Vol 249 (962) ◽  
pp. 151-177 ◽  
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Strong Convergence ◽  
Resolvent Operator ◽  
Infinitesimal Generator ◽  
Semigroups Of Operators ◽  
Ergodic Theorems ◽  
Semigroup Of Operators ◽  
Ergodic Properties ◽  
The Resolvent Operator

If ^ = {7^: t ^0} is a one-parameter semigroup of operators on a Banach space X , an element x of X is called ergodic if T t X has a generalized limit as t -> oo. It is shown, for a wide class of semigroups, that the use of Abel or Cesaro limits, and of weak or strong convergence, leads to four equivalent definitions of ergodicity. When the resolvent operator of G has suitable compactness properties, every element of X is ergodic. The ergodic properties of G can be completely determined when its infinitesimal generator is known. Some of these results can be extended to more generaltypes of weak convergence in X , and this leads to a discussion of ergodic properties of the semigroup adjoint to G

Semigroups of Operators on Hardy Spaces and Cocycles of Holomorphic Flows

2010 ◽  
Vol 6 (1) ◽  
pp. 113-119
Author(s):  
Farhad Jafari ◽  
Zbigniew Slodkowski ◽  
Thomas Tonev
Keyword(s):  
Hardy Spaces ◽  
Semigroups Of Operators
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