Geodesic
An extension of Lorentz's almost convergence and applications in Banach spaces
Serdica Mathematical Journal, Tome 32 (2006) no. 1, pp. 71-98 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

Voir la notice de l'article

We investigate an extension of the almost convergence of G. G. Lorentz requiring that the means of a bounded sequence converge uniformly on a subset M of N. We also present examples of sequences α∈ l∞(N) whose sequences of translates (Tn α)n≥ 0 (where T is the left-shift operator on l∞(N)) satisfy: (a) Tn α, n ≥ 0 generates a subspace E(α) of l∞(N) that is isomorphically embedded into c0 while α is not almost convergent. (b) Tn α, n ≥ 0 admits an l1-subsequence and a nontrivial weakly Cauchy subsequence while a is almost convergent. Finally we show that, in the sense of measure, for almost all real sequences taking values in a compact set K ⊆ R (with at least two points), the sequence (Tn α)n ≥ 0 is equivalent in the supremum norm to the usual l1-basis and (hence) not almost convergent.
Keywords: Almost Convergence, Banach Limit, Weakly Cauchy Sequence, Independent Sequence, Uniform Distribution of Sequences 
@article{SMJ2_2006_32_1_a6,
     author = {Mercourakis, S. and Vassiliadis, G.},
     title = {An extension of {Lorentz's} almost convergence and applications in {Banach} spaces},
     journal = {Serdica Mathematical Journal},
     pages = {71--98},
     year = {2006},
     volume = {32},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2006_32_1_a6/}
}
TY  - JOUR
AU  - Mercourakis, S.
AU  - Vassiliadis, G.
TI  - An extension of Lorentz's almost convergence and applications in Banach spaces
JO  - Serdica Mathematical Journal
PY  - 2006
SP  - 71
EP  - 98
VL  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2006_32_1_a6/
LA  - en
ID  - SMJ2_2006_32_1_a6
ER  - 
%0 Journal Article
%A Mercourakis, S.
%A Vassiliadis, G.
%T An extension of Lorentz's almost convergence and applications in Banach spaces
%J Serdica Mathematical Journal
%D 2006
%P 71-98
%V 32
%N 1
%U http://geodesic.mathdoc.fr/item/SMJ2_2006_32_1_a6/
%G en
%F SMJ2_2006_32_1_a6
Mercourakis, S.; Vassiliadis, G. An extension of Lorentz's almost convergence and applications in Banach spaces. Serdica Mathematical Journal, Tome 32 (2006) no. 1, pp. 71-98. http://geodesic.mathdoc.fr/item/SMJ2_2006_32_1_a6/