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ENTROPY NUMBERS OF DIAGONAL OPERATORS BETWEEN VECTOR-VALUED SEQUENCE SPACES

Published online by Cambridge University Press:  30 January 2002

THOMAS KÜHN  and
TOMAS P. SCHONBEK
THOMAS KÜHN
Affiliation:
Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany; [email protected]
TOMAS P. SCHONBEK
Affiliation:
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA; [email protected]
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Abstract

Upper and lower bounds are established for the entropy numbers of certain diagonal operators between Banach sequence spaces. These diagonal operators are isomorphisms between the spaces considered in the paper and weighted sequence spaces considered by Leopold so that the entropy numbers in question coincide with those considered by Leopold. The results in the paper improve the previous results in at least two ways. The estimates in the paper are ‘almost’ sharp in the sense that the upper and lower estimates differ only by logarithmic factors for a much wider range of parameters. Moreover, all the upper estimates are improvements on the previous ones, the improvement being quite significant in some cases.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 739 - 754
Copyright
London Mathematical Society 2001

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