Lotz-Rabiger's nets of Markov operators in L-1-spaces

Emel'yanov E., Erkursun N.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.371, no.2, pp.777-783, 2010 (SCI-Expanded) identifier identifier


The Lotz-Rabiger nets (LR-nets) introduced in Rabiger (1993) [18] under the name M-nets provide an appropriate setting for investigation various mean ergodic theorems in Banach spaces. In the present paper we prove several convergence theorems for LR-nets of Markov operators in L-1-spaces which extend Theorems 1 and 5 from Emel'yanov (2004) [8]. and Theorem 1.1 from Lasota (1983) [11]. (C) 2010 Elsevier Inc. All rights reserved.