We determine the asymptotic behavior of the entropy numbers of diagonal operators D: lp → lq, (xk) → (skxk), 0 < p,q ≤ ∞, under mild regularity and decay conditions on the generating sequence (σk). Our results extend the known estimates for polynomial and logarithmic diagonals (σk). Moreover, we also consider some exotic intermediate examples like (σk)=exp(-√log k).
@article{urn:eudml:doc:44542,
title = {Entropy numbers of general diagonal operators.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {18},
year = {2005},
pages = {479-491},
zbl = {1093.47020},
mrnumber = {MR2166521},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44542}
}
Kühn, Thomas. Entropy numbers of general diagonal operators.. Revista Matemática de la Universidad Complutense de Madrid, Tome 18 (2005) pp. 479-491. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44542/