Geodesic
Sur la Convergence Ponctuelle de Quelques Suites D'Operateurs
Canadian mathematical bulletin, Tome 30 (1987) no. 2, pp. 134-141

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

Let (αn.k) be a sequence of positive numbers. We define a regular sequence (resp. a weakly regular sequence) and then show the existence of a unitary operator (resp. a contraction T) L 2[0, 1] → L 2[0, 1] and a function f ∊ L2[0, 1] such that the pointwise convergence of the sequence of functions is not satisfied almost surely. As a first corollary the pointwise convergence of the Abel means of a contraction from L2 into L2 does not hold necessarily almost surely. As a second corollary there exists a contraction T for which the means (and powers) of Brunei's operator A do not converge pointwise a.s. We also show that, for P > 1 fixed, there exists a sequence of positive numbers αn.k for which we have the pointwise convergence in LP of the sequence of polynomials where T is a contraction of L1 and L α. The dominated theorem does not, however, always hold for such LP-contractions.
DOI : 10.4153/CMB-1987-020-7
Mots-clés : 47A35 
Assani, I. Sur la Convergence Ponctuelle de Quelques Suites D'Operateurs. Canadian mathematical bulletin, Tome 30 (1987) no. 2, pp. 134-141. doi: 10.4153/CMB-1987-020-7
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