Strictly singular operators in pairs of  L   p   space

E. M. Semenov; P. Tradacete; F. L. Hernandez

doi:10.1134/S1064562416040281

Strictly singular operators in pairs of L_p space

Authors: Semenov E.M.¹, Tradacete P.², Hernandez F.L.³
Affiliations:
1. Voronezh State University
2. Universidad Carlos III de Madrid
3. Complutense University of Madrid
Issue: Vol 94, No 1 (2016)
Pages: 450-452
Section: Mathematics
URL: https://journals.rcsi.science/1064-5624/article/view/224106
DOI: https://doi.org/10.1134/S1064562416040281
ID: 224106

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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 Q ⊂ E, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from L_p to L_q is found. There exists a strictly singular but not superstrictly singular operator on L_p, provided that p ≠ 2.