Strictly singular operators in pairs of Lp space
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- Semenov, E.M., Tradacete, P. & Hernandez, F.L. Dokl. Math. (2016) 94: 450. doi:10.1134/S1064562416040281
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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 Lp to Lq is found. There exists a strictly singular but not superstrictly singular operator on Lp, provided that p ≠ 2.