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Domains of integral operators

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It is shown that the proper domains of integral operators have separating duals but in general they are not locally convex. Banach function spaces which can occur as proper domains are characterized. Some known and some new results are given, illustrating the usefulness of the notion of proper domain.
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  • Department of Mathematics, University of Mississippi, Oxford, ,Mississippi 38677, U.S.A.
  • Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, U.S.A.
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