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The nuclearity of operators generated by Hölder continuous kernels

Published online by Cambridge University Press:  24 October 2008

James Alan Cochran
James Alan Cochran
Affiliation:
Department of Mathematics Virginia Polytechnic Institute and State University Blacksburg, Virginia 24061
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Introduction. The space Cp is the class of operators on a Hilbert space for which the norm ∥K∥p = [trace (KK*)P/2]/p is finite. Equivalently, a compact operator is in Cp if

where the μn are the so-called ‘singular values’ of K (characteristic values of the non-negative compact operator [K] ≡ (KK*)½). The case p = 2 gives the familiar class of Hilbert–Schmidt operators, while C1 is the collection of trace-class or nuclear operators considered by Schatten(12), Lidskii(11), and Gohberg and Krein(7), among others.

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Type
Research Article
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Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 3 , May 1974 , pp. 351 - 356
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

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