Optimal and one-complemented subspaces. (English) Zbl 1147.46017

Lewicki, Grzegorz; Trombetta, Giulio

Monatsh. Math. 153, No. 2, 115-132 (2008).

Authors’ abstract: Let \(X\) be a real Banach space and let \(V \subset X\) be a closed linear subspace. In [B.Beauzamy and B.Maurey, J. Funct.Anal.24, 107–139 (1977; Zbl 0344.46049), Prop.5] it was proven that if \(X\) is strictly convex, reflexive and smooth and \(V\) is an optimal subset of \(X\), then \(V\) is one-complemented in \(X\). In this note, we extend this result to non-smooth Banach spaces. In particular, we show that any existence subspace of \(c, c_{0}\) or \(l_{1}\) is one-complemented. Also, some results concerning non-smooth Musielak-Orlicz sequence spaces equipped with the Luxemburg norm are presented.

Reviewer: Satit Saejung (Khon Kaen)

MSC:

46B45

Banach sequence spaces

Keywords:

Musielak-Orlicz space; one complemented subspace; optimal set

Citations:

Zbl 0344.46049

References:

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