Unconditional ideals of finite rank operators II

• Autores: Trond A. Abrahamsen, Vegard Lima, Asvald Lima
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 35, Nº 2, 2009, págs. 627-646
• Idioma: inglés
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• Resumen

  • Let E be a subspace of a normed space F. It is known that E is an ideal (resp. a u-ideal) in F if and only if E is an ideal (resp. a u-ideal) in G for every subspace E?G?F in which E has finite codimension (resp. codimension = 2). We show that in many cases a space of finite rank operators is an ideal (resp. a u-ideal) in a larger space if and only if it is an ideal (resp. a u-ideal) in a space in which it has codimension 1. In particular, we show that F(Y,X) is an ideal (resp. a u-ideal) in W(Y,X**) for all Banach spaces Y if and only if for every reflexive Banach space Y and T?W(Y,X**), F(Y,X) is an ideal (resp. a u-ideal) in span( F(Y,X),{T}).