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Strictly singular operators on Lp spaces and interpolation

Impacto

Hernández, Francisco L. y Semenov, Evgeny M. y 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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URL Oficial: http://www.ams.org/journals/proc/2010-138-02/S0002-9939-09-10089-8/S0002-9939-09-10089-8.pdf




Resumen

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.


Tipo de documento:Artículo
Palabras clave:Strictly singular operator; Lp space; interpolation; ideals
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:15986
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