Three-space problems and bounded approximation properties
Wolfgang Lusky (2003)
Studia Mathematica
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Let 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 -space, then both X and A have bases. We apply these results to show that the spaces and have bases whenever Λ ⊂ ℤ and ℤ∖Λ is a Sidon set.