Injective Banach spaces of typeC(T)
Tóm tắt
A Banach spaceX is aP
λ-space if wheneverX is isometrically embedded in another Banach spaceY there is a projection ofY ontoX with norm at most λ.C(T) denotes the Banach space of continuous real-valued functions on the compact Hausdorff spaceT. T satisfies the countable chain condition (CCC) if every family of disjoint non-empty open sets inT is countable.T is extremally disconnected if the closure of every open set inT is open. The main result is that ifT satisfies the CCC andC(T) is aP
λ-space, thenT is the union of an open dense extremally disconnected subset and a complementary closed setT
Asuch thatC(TA) is aP
λ−1-space.
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