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Siberian Mathematical Journal

, Volume 54, Issue 3, pp 479–486 | Cite as

Measure-compact operators, almost compact operators, and linear functional equations in L p

  • V. B. Korotkov
Article

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

almost compact operator measure-compact operator integral operator Carleman operator linear functional equation of the second kind in Lp linear integral equations in Lp 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • V. B. Korotkov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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