Doklady Mathematics

, Volume 94, Issue 1, pp 450–452 | Cite as

Strictly singular operators in pairs of Lp space

Mathematics

Abstract

Let E and F be Banach spaces. A linear operator from E to F is said to be strictly singular if, for any subspace QE, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from Lp to Lq is found. There exists a strictly singular but not superstrictly singular operator on Lp, provided that p ≠ 2.

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • E. M. Semenov
    • 1
  • P. Tradacete
    • 2
  • F. L. Hernandez
    • 3
  1. 1.Voronezh State UniversityVoronezhRussia
  2. 2.Universidad Carlos III de MadridMadridSpain
  3. 3.Complutense University of MadridMadridSpain

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