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Optimal and one-complemented subspaces

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Abstract.

Let X be a real Banach space and let V ⊂ X be a closed linear subspace. In [4, Prop. 5] it has been 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 would like to extend this result to non-smooth Banach spaces. In particular, we show that any existence subspace of c,c o and l 1 is one-complemented. Also some results concerning non-smooth Musielak-Orlicz sequence spaces equipped with the Luxemburg norm will be presented.

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Authors and Affiliations

  1. Jagiellonian University, Kraków, Poland

    Grzegorz Lewicki

  2. University of Calabria, Cosenza, Italy

    Giulio Trombetta

Authors
  1. Grzegorz Lewicki
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  2. Giulio Trombetta
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Additional information

The first author was supported by Polish State Committee for Scientific Research Grant KBN 1 PO3A O10 26.

Authors’ addresses: Grzegorz Lewicki, Department of Mathematics, Jagiellonian University, 30-059 Kraków, Reymonta 4, Poland; Giulio Trombetta, Department of Mathematics, University of Calabria, 87036 Arcavacata di Rende, Cosenza, Italy

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Lewicki, G., Trombetta, G. Optimal and one-complemented subspaces. Monatsh Math 153, 115–132 (2008). https://doi.org/10.1007/s00605-007-0510-4

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  • DOI: https://doi.org/10.1007/s00605-007-0510-4

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