Ergodic theorem for sequences in a Hilbert space

摘要

By suitability modifying our methods, we prove the following nonlinear ergodic theorem, extending H. Brezis and F.E. Browder and R. Wittmann's mean ergodic theorem. For any sequence (x(sub n)) n (>=) 0 in a real Hilbert space H satisfying: (x(sub j) modul x(sub j)+l) (<=) (x(sub k) modul x(sub k+l)) + (epsilon) (k,l,j-k) for all k,l (>=) 0 and j (>=) k with (epsilon) bounded and (epsilon) tends to zero for k, l, m (yields) (infinity), and any strongly regular summation method (l brace)a(sub n,j)(r brace), the sequence y(sub n) = (Sigma)(sup (infinity))(sub j=0) a(sub n,j) x(sub j) converges strongly to the same limit. Some identifications of the limit are also given. (author). 15 refs. (Atomindex citation 27:046091)