Three-space problems and bounded approximation properties

Wolfgang Lusky

Wolfgang Lusky

Studia Mathematica, Tome 157 (2003), p. 417-434 / Harvested from The Polish Digital Mathematics Library

Résumé

Let ${R ₙ}_{n = 1}^{\infty}$ be a commuting approximating sequence of the Banach space X leaving the closed subspace A ⊂ X invariant. Then we prove three-space results of the following kind: If the operators Rₙ induce basis projections on X/A, and X or A is an $ℒ_{p}$ -space, then both X and A have bases. We apply these results to show that the spaces $C_{Λ} = \bar{s p a n} z^{k} : k \in Λ \subset C ()$ and $L_{Λ} = \bar{s p a n} z^{k} : k \in Λ \subset L ₁ ()$ have bases whenever Λ ⊂ ℤ and ℤ∖Λ is a Sidon set.

Publié le : 2003-01-01

Zbl 1055.46008

EUDML-ID : urn:eudml:doc:284452

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-3-6,
     author = {Wolfgang Lusky},
     title = {Three-space problems and bounded approximation properties},
     journal = {Studia Mathematica},
     volume = {157},
     year = {2003},
     pages = {417-434},
     zbl = {1055.46008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-3-6}
}

Wolfgang Lusky. Three-space problems and bounded approximation properties. Studia Mathematica, Tome 157 (2003) pp. 417-434. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-3-6/