Almost compactness and decomposability of integral operators
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- by Walter Schachermayer and Lutz Weis PDF
- Proc. Amer. Math. Soc. 81 (1981), 595-599 Request permission
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.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- 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