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

Entropy Numbers of General Diagonal Operators

Thomas KÜHN
Mathematisches Institut
Universität Leipzig
Augustusplatz 10-11
D-04109 Leipzig — Germany
kuehn@math.uni-leipzig.de

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

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.