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Proceedings of the American Mathematical Society

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

 

 

Lattice properties of integral operators


Author: Lawrence Lessner
Journal: Proc. Amer. Math. Soc. 72 (1978), 497-500
MSC: Primary 47B38; Secondary 47G05
DOI: https://doi.org/10.1090/S0002-9939-1978-0509241-4
MathSciNet review: 509241
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Abstract: In this paper we are concerned with linear operators $ K:L \to M$, where L is a Riesz subspace of measurable, finite a.e. functions and M is the class of all measurable, finite a.e. functions defined by $ k(x,y)$ is a measurable kernel. It will be shown that the class $ I[L,M]$ of all such integral operators is a Dedekind complete Riesz space, an ideal and a band in the space of order bounded linear maps $ T:L \to M$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0509241-4
Article copyright: © Copyright 1978 American Mathematical Society