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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Metric entropy conditions for an operator to be of trace class
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by José M. González-Barrios and Richard M. Dudley
Proc. Amer. Math. Soc. 118 (1993), 175-180
DOI: https://doi.org/10.1090/S0002-9939-1993-1145418-3

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.
References
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Bibliographic Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 118 (1993), 175-180
  • MSC: Primary 47B10; Secondary 47G10, 60B11, 60G15, 60G17
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1145418-3
  • MathSciNet review: 1145418