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Almost compactness and decomposability of integral operators


Authors: Walter Schachermayer and Lutz Weis
Journal: Proc. Amer. Math. Soc. 81 (1981), 595-599
MSC: Primary 47G05; Secondary 45P05, 47B05, 47B38
DOI: https://doi.org/10.1090/S0002-9939-1981-0601737-X
MathSciNet review: 601737
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Abstract: Let $ (X,\mu )$, $ (Y,v)$ be finite measure spaces and $ 1 < q \leqslant \infty $, $ 1 \leqslant p \leqslant q$. An integral operator $ \operatorname{Int}(k):{L^q}(v) \to {L^p}(\mu )$ becomes compact, if we cut away a suitably chosen subset of $ X$ of arbitrarily small measure. As a consequence we prove that $ \operatorname{Int}(k)$ may be written as the sum of a Carleman operator and an orderbounded integral operator, where the orderbounded part may be chosen to be compact and of arbitrarily small norm.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0601737-X
Keywords: Integral operator
Article copyright: © Copyright 1981 American Mathematical Society

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