On Lindenstrauss-Pełczyński spaces

الأصل · EN

In this work we shall be concerned with 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 the converse. 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. Complemented subspaces of C(K) and separably injective spaces are subclasses of LP-spaces and we show that the former does not contain the latter. It is established that L∞-spaces not containing l₁ are quotients of LP-spaces, while L∞-spaces not containing c₀, quotients of an LP-space by a separably injective space and twisted sums of LP-spaces are LP-spaces.