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Strictly singular operators on Lp spaces and interpolation

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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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Official URL: http://www.ams.org/journals/proc/2010-138-02/home.html


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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
Deposited On:18 Jul 2012 08:56
Last Modified:27 Jun 2018 07:28

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