Sur les isométries de \(L^ p(X)\) et le théorème ergodique vectoriel. (On the isometries of \(L^ p(X)\) and the vectorial ergodic theorem). (French) Zbl 0644.46025
Let \(1<p<+\infty\), X a reflexive Banach space and T an isometry of \(L^ p(X)\). We give a representation of those isometries and we prove that T verifies a maximal inequality and the\(\lim _{\to}A_ n\), is liminal if and only if for any decreasing sequence of minimal projections \(p_ n\in A_ n\), a certain sequence of numbers, \(d_ n\), is eventually constant. Here \(d_ n\) is the number of minimal orthogonal projections in \(A_ n\) which are equivalent to \(p_ n\).
Reviewer: J.Kaminker
