Abel-ergodic theorems for subsequences

Ryōtarō Satō

Vol. 47 (1973), No. 1, 233–242

DOI: 10.2140/pjm.1973.47.233

Abstract

Let T be a positive linear contraction on an L¹-space and k₁,k₂,⋯ an increasing sequence of positive integers. In this paper the almost everywhere convergence of Abel averages ∑ _i=1^∞r^k_iT^k_if∕∑_i=1^∞r^k_i for the sequence k₁,k₂,⋯ as r ↑ 1 is investigated.

Mathematical Subject Classification 2000

Primary: 28A65

Secondary: 47A35

Milestones

Received: 10 March 1972

Published: 1 July 1973