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Strictly singular operators on Lp spaces and interpolation

Hernández, Francisco L. and Semenov, Evgeny M. and Tradacete Pérez, Pedro (2010) Strictly singular operators on Lp spaces and interpolation. Proceedings of the American Mathematical Society, 138 (2). pp. 675-686. ISSN 0002-9939

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Abstract

We study the class Vp of strictly singular non-compact operators on Lp spaces. This allows us to obtain interpolation results for strictly singular operators on Lp spaces. Given 1 ≤ p < q ≤ ∞, it is shown that if an operator T bounded on Lp and Lq is strictly singular on Lr for some p ≤ r ≤ q, then it is compact on Ls for every p < s < q.

Item Type:Article
Uncontrolled Keywords:Strictly singular operator; Lp space; interpolation; ideals
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15986
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