Monatshefte für Mathematik

, Volume 136, Issue 2, pp 87–97

On Subspaces and Quotients of Banach Spaces C(K, X)

  • Elói Medina Galego

Abstract.

 We study the relation of \(\) to the subspaces and quotients of Banach spaces of continuous vector-valued functions \(\), where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of \(\) totally incomparable to X contains a copy of \(\) complemented in \(\). This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of \(\) which contain no copy of \(\) are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of \(\) which is quotient incomparable to X, contains a complemented copy of \(\). Finally we present some more geometric properties of \(\) spaces.

2000 Mathematics Subject Classification: 46B03 46B20 46E15 
Key words: Banach spaces of continuous vector-valued functions 

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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Elói Medina Galego
    • 1
  1. 1.University of São Paulo, BrazilBR

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