Quelques théorèmes ergodiques dans les espaces \(L^ p_ E\). (Some ergodic theorems in \(L^ p_ E\) spaces) (Q1822403)

Let E be a separable Banach space and T be a linear and power bounded operator on \(L^ p_ E[0,1]\), \(1<p<\infty\). Some dominated and pointwise ergodic theorems for the operator T are proved. Necessary and sufficient conditions to get the pointwise convergence of the Cesaro means \(n^{-1}(I+T+...+T^ n)(f)\) of a function \(f\in L^ p_ E[0,1]\) are given.