Strict u-ideals in Banach spaces

Vegard Lima; Åsvald Lima

Studia Mathematica, Tome 192 (2009), p. 275-285 / Harvested from The Polish Digital Mathematics Library

Résumé

We study strict u-ideals in Banach spaces. A Banach space X is a strict u-ideal in its bidual when the canonical decomposition $X * * * = X * \oplus X^{⊥}$ is unconditional. We characterize Banach spaces which are strict u-ideals in their bidual and show that if X is a strict u-ideal in a Banach space Y then X contains c₀. We also show that $ℓ_{\infty}$ is not a u-ideal.

Publié le : 2009-01-01

Zbl 1190.46015

EUDML-ID : urn:eudml:doc:284886

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Vegard Lima; Åsvald Lima. Strict u-ideals in Banach spaces. Studia Mathematica, Tome 192 (2009) pp. 275-285. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-3-6/