Compactness criteria for integral operators in and
spaces
Author:
S. P. Eveson
Journal:
Proc. Amer. Math. Soc. 123 (1995), 3709-3716
MSC:
Primary 47B38; Secondary 47B07, 47G10
DOI:
https://doi.org/10.1090/S0002-9939-1995-1291766-8
MathSciNet review:
1291766
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a positive measure space,
be a measurable function such that the kernel
induces a bounded integral operator on
(equivalently, that
), and for
let
. We show that it is sufficient for the integral operator T induced by k on
to be compact, that there exists a locally
-null set
such that the set
is relatively compact in
, and that this condition is also necessary if
is separable. In the case of Lebesgue measure on a subset of
, we use Riesz's characterisation of compact sets in
to provide a more tractable form of this criterion.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1995-1291766-8
Article copyright:
© Copyright 1995
American Mathematical Society