Geodesic
Pointwise Convergence of Alternating Sequences
Canadian journal of mathematics, Tome 40 (1988) no. 3, pp. 610-632

Voir la notice de l'article provenant de la source Cambridge University Press

Let 1 < p < ∞ and let Lp be the usual Banach Space of complex valued functions on a σ-finite measure space. Let (Tn), n ≧ 1, be a sequence of positive linear contractions on Lp . Hence and , where is the part of Lp that consists of non-negative Lp functions. The adjoint of Tn is denoted by which is a positive linear contraction of Lq with q = p/(p — 1).Our purpose in this paper is to show that the alternating sequences associated with (Tn), as introduced in [2], converge almost everywhere. Complete definitions will be given later. When applied to a non negative function, however, this result is reduced to the following theorem.(1.1) THEOREM. If (Tn) is a sequence of positive contractions of Lp then (1.2) exists a.e. for all. 
Akcoglu, M. A.; Sucheston, L. Pointwise Convergence of Alternating Sequences. Canadian journal of mathematics, Tome 40 (1988) no. 3, pp. 610-632. doi: 10.4153/CJM-1988-026-4
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