The Hopf decomposition and the individual divergence to \(\infty\) on a band (Q1206981)

Recently, the author has extended a ratio ergodic theorem of Ornstein to Archimedean Riesz spaces, and in doing so, has defined several types of convergence and divergence in Riesz spaces, one of them being the individual divergence to \(\infty\) on a band. In the note the author uses the notion of individual divergence to \(\infty\) on a band in order to obtain a new approach to the Hopf decomposition and to extend one of his previous results concerning the Hopf decomposition in ordered vector spaces.