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## Studia Mathematica

2009 | 194 | 2 | 105-115
Tytuł artykułu

### The structure of Lindenstrauss-Pełczyński spaces

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Lindenstrauss-Pełczyński (for short ℒ𝒫) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ𝒫-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides a negative answer to a problem posed by Lindenstrauss and Pełczyński [J. Funct. Anal. 8 (1971)]. We show that the class of ℒ𝒫-spaces does not have the 3-space property, which corrects a theorem in an earlier paper of the authors [Studia Math. 174 (2006)]. We then solve a problem in that paper showing that $ℒ_{∞}$ spaces not containing l₁ are not necessarily ℒ𝒫-spaces.
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Tom
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105-115
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2009
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