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Título:
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Disjointly strictly-singular inclusions between rearrangement invariant spaces
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Autores:
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García del Amo Jiménez, Alejandro José ;
Hernández, Francisco L. ;
Sánchez de los Reyes, Víctor Manuel ;
Semenov, Evgeny M.
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Tipo de documento:
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texto impreso
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Editorial:
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London Mathematical Society, 2000
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Análisis funcional y teoría de operadores
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Tipo = Artículo
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Resumen:
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A linear operator between two Banach spaces X and Y is strictly-singular (or Kato) if it fails to be an isomorphism on any infinite dimensional subspace. A weaker notion for Banach lattices introduced in [8] is the following one: an operator T from a Banach lattice X to a Banach space Y is said to be disjointly strictly-singular if there is no disjoint sequence of non-null vectors (xn)n?N in X such that the restriction of T to the subspace [(xn)?n=1] spanned by the vectors (xn)n?N is an isomorphism. Clearly every strictly-singular operator is disjointly strictly-singular but the converse is not true in general (consider for example the canonic inclusion Lq[0, 1]?Lp[0, 1] for 1?p
The aim of this paper is to study when the inclusion operators between arbitrary rearrangement invariant function spaces E[0, 1] ? E on the probability space [0, 1] are disjointly strictly-singular operators.
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