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

DOI

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
@article{10_4153_CMB_1987_020_7,
     author = {Assani, I.},
     title = {Sur la {Convergence} {Ponctuelle} de {Quelques} {Suites} {D'Operateurs}},
     journal = {Canadian mathematical bulletin},
     pages = {134--141},
     year = {1987},
     volume = {30},
     number = {2},
     doi = {10.4153/CMB-1987-020-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-020-7/}
}
TY  - JOUR
AU  - Assani, I.
TI  - Sur la Convergence Ponctuelle de Quelques Suites D'Operateurs
JO  - Canadian mathematical bulletin
PY  - 1987
SP  - 134
EP  - 141
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-020-7/
DO  - 10.4153/CMB-1987-020-7
ID  - 10_4153_CMB_1987_020_7
ER  - 
%0 Journal Article
%A Assani, I.
%T Sur la Convergence Ponctuelle de Quelques Suites D'Operateurs
%J Canadian mathematical bulletin
%D 1987
%P 134-141
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-020-7/
%R 10.4153/CMB-1987-020-7
%F 10_4153_CMB_1987_020_7

Cité par Sources :