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Onl p-complemented copies in Orlicz spaces II

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Abstract

For anyp > 1, the existence is shown of Orlicz spacesL F andl F with indicesp containingsingular l p-complemented copies, extending a result of N. Kalton ([6]). Also the following is proved:Let 1 <α ≦β < ∞and H be an arbitrary closed subset of the interval [α, β].There exist Orlicz sequence spaces l F (resp. Orlicz function spaces LF)with indices α and β containing only singular l p-complemented copies and such that the set of values p > 1for which l p is complementably embedded into lF (resp. L F)is exactly the set H (resp. H ∪ {2&#x007D;). An explicitly defined class of minimal Orlicz spaces is given.

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Authors and Affiliations

  1. Dpto. Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040, Madrid, Spain

    Francisco L. Hernández & Baltasar Rodriguez-Salinas

Authors
  1. Francisco L. Hernández
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  2. Baltasar Rodriguez-Salinas
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Supported in part by CAICYT grant 0338-84.

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Hernández, F.L., Rodriguez-Salinas, B. Onl p-complemented copies in Orlicz spaces II. Israel J. Math. 68, 27–55 (1989). https://doi.org/10.1007/BF02764967

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  • DOI: https://doi.org/10.1007/BF02764967

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