Strictly singular operators in pairs of L p space
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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 L p to L q is found. There exists a strictly singular but not superstrictly singular operator on L p , provided that p ≠ 2.
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