Uniform convergence in the individual ergodic theorem for symmetric sequence spaces

Abstract

It is proved that for any Dunford-Schwartz operator $T$ acting in the space $l_{\infty }$ and for each $x\in c_0$ there exists an element $\hat{x}\in c_0$ such that $\Vert \frac{1}{n}{\sum }_{k=0}^{n-1}{T}^k(x)-\hat{x}{\Vert }_{\infty }\to 0$.

References in corpus (1)

• Pointwise ergodic theorems in symmetric spaces of measurable functions