Full paper in PDF:
$%T. Kühn, Entropy numbers of general diagonal operators, Rev. Mat. Complut. 18 (2005), no. 2, 479–491.%$

Entropy Numbers of General Diagonal Operators

Thomas KÜHN
Mathematisches Institut
Universität Leipzig
Augustusplatz 10-11
D-04109 Leipzig Germany

Received: February 10, 2005
Accepted: April 26, 2005

We determine the asymptotic behavior of the entropy numbers of diagonal operators D :lp-- > lq  , (xk) '--> (skxk)  , 0 < p,q < oo  , under mild regularity and decay conditions on the generating sequence (sk)  . Our results extend the known estimates for polynomial and logarithmic diagonals (sk)  . Moreover, we also consider some exotic intermediate examples like           V~ ---
sk = exp(- logk)  .

Key words: entropy numbers, diagonal operators, lp  -spaces.
2000 Mathematics Subject Classification:
47B06, 46B45.