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Measure-compact operators, almost compact operators, and linear functional equations in L p
Authors:V B Korotkov
Institution:13013. Sobolev Institute of Mathematics, Novosibirsk, Russia
Abstract:Under study are the measure-compact operators and almost compact operators in L p . We construct an example of a measure-compact operator that is not almost compact. Introducing two classes of closed linear operators in L p , we prove that the resolvents of these operators are almost compact or measure-compact. We present methods for the reduction of linear functional equations of the second kind in L p with almost compact or measure-compact operators to equivalent linear integral equations in L p with quasidegenerate Carleman kernels.
Keywords:
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