Ideals of compact operators

• Autores: Asvald Lima, Eve Oja
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 77, Nº 1, 2004, págs. 91-110
• Idioma: inglés
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• Resumen

  • We give an example of a Banach space such that is not an ideal in . We prove that if is a weak denting point in the unit ball of and if is a closed subspace of a Banach space , then the set of norm-preserving extensions of a functional is equal to the set . Using this result, we show that if is an -ideal in and is a reflexive Banach space, then is an -ideal in whenever is an ideal in . We also show that is an ideal (respectively, an -ideal) in for all Banach spaces whenever is an ideal (respectively, an -ideal) in and has the compact approximation property with conjugate operators.