Strictly singular operators on 𝐿_{𝑝} spaces and interpolation

Hernández, Francisco; Semenov, Evgeny; Tradacete, Pedro

doi:10.1090/S0002-9939-09-10089-8

Strictly singular operators on $L_p$ spaces and interpolation
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by Francisco L. Hernández, Evgeny M. Semenov and Pedro Tradacete PDF

Proc. Amer. Math. Soc. 138 (2010), 675-686 Request permission

Abstract:

We study the class $V_p$ of strictly singular non-compact operators on $L_p$ spaces. This allows us to obtain interpolation results for strictly singular operators on $L_p$ spaces. Given $1\leqslant p<q\leqslant \infty$, it is shown that if an operator $T$ bounded on $L_p$ and $L_q$ is strictly singular on $L_r$ for some $p\leqslant r\leqslant q$, then it is compact on $L_s$ for every $p<s<q$.

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