Summary
We prove that, when X is one of the Banach spaces lp (1⩽p⩽ ∞) or c0, then every infinite-dimensional complemented subspace of XN (resp. X(N)) is isomorphic to one of the following spaces: (ω, X, ω × X, XN (resp. ϕ, X, ϕ ⊕ X, X(N)). Therefore, XN and X(N) are primary. We also give some consequences and related results.
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The second author acknowledges partial support from the Italian Ministero della Pubblica Istruzione.
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Metafune, G., Moscatelli, V.B. Complemented subspaces of sums and products of banach spaces. Annali di Matematica pura ed applicata 153, 175–190 (1988). https://doi.org/10.1007/BF01762391
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DOI: https://doi.org/10.1007/BF01762391