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Complemented copies of \(c_ 0\) in vector-valued Köthe-Dieudonné function spaces. (English) Zbl 0782.46035

Let \(\Lambda\) be a barrelled perfect Köthe space of measurable functions defined on an atomless finite Radon measure space. [This class of function spaces was defined by J. Dieudonné, “Sur les espaces de Köthe”, J. Analyse Math. 1, 81-115 (1951; Zbl 0044.117)]. Let \(X\) be a Banach space containing a copy of \(c_ 0\), then the space \(\Lambda(X)\) of \(\Lambda\)-Bochner integrable functions contains a complemented copy of \(c_ 0\).
Reviewer: S.Díaz (Sevilla)

MSC:

46E40 Spaces of vector- and operator-valued functions
46B25 Classical Banach spaces in the general theory
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Citations:

Zbl 0044.117
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