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## Studia Mathematica

2006 | 174 | 3 | 213-231
Tytuł artykułu

### On Lindenstrauss-Pełczyński spaces

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EN
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EN
We consider some stability aspects of the classical problem of extension of C(K)-valued operators. We introduce the class ℒ𝒫 of Banach spaces of Lindenstrauss-Pełczyński type as those such that every operator from a subspace of c₀ into them can be extended to c₀. We show that all ℒ𝒫-spaces are of type $ℒ_{∞}$ but not conversely. Moreover, $ℒ_{∞}$-spaces will be characterized as those spaces E such that E-valued operators from w*(l₁,c₀)-closed subspaces of l₁ extend to l₁. Regarding examples we will show that every separable $ℒ_{∞}$-space is a quotient of two ℒ𝒫-spaces; also, $ℒ_{∞}$-spaces not containing c₀ are ℒ𝒫-spaces; the complemented subspaces of C(K) and the separably injective spaces are subclasses of the ℒ𝒫-spaces and we show that the former does not contain the latter. Regarding stability properties, we prove that quotients of an ℒ𝒫-space by a separably injective space and twisted sums of ℒ𝒫-spaces are ℒ𝒫-spaces.
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Tom
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213-231
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wydano
2006
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