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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Metric entropy conditions for an operator to be of trace class


Authors: José M. González-Barrios and Richard M. Dudley
Journal: Proc. Amer. Math. Soc. 118 (1993), 175-180
MSC: Primary 47B10; Secondary 47G10, 60B11, 60G15, 60G17
MathSciNet review: 1145418
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Abstract: Let $ A$ be an operator from one Hilbert space $ H$ into another. It was known that $ A$ is of trace class if and only if the metric entropy of $ A(B)$ is integrable where $ B$ is the unit ball in $ H$. We give a new, general sufficient condition for an integral operator to be of trace class, and examples showing it is sharp but not necessary.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1145418-3
PII: S 0002-9939(1993)1145418-3
Keywords: Metric entropy, ellipsoids, trace class, Hilbert-Schmidt operators
Article copyright: © Copyright 1993 American Mathematical Society