Mathematische Annalen

, Volume 333, Issue 4, pp 831–858 | Cite as

Operators on C[0,1] preserving copies of asymptotic ℓ1 spaces

  • I. GasparisEmail author


Given separable Banach spaces X, Y, Z and a bounded linear operator T:XY, then T is said to preserve a copy of Z provided that there exists a closed linear subspace E of X isomorphic to Z and such that the restriction of T to E is an into isomorphism. It is proved that every operator on C([0,1]) which preserves a copy of an asymptotic ℓ1 space also preserves a copy of C([0,1]).


Operators on C(K) space asymptotic ℓ1 space weakly null sequence Schreier sets 

Mathematics Subject Classification (2000)

Primary: 46B03 Secondary: 06A07 03E02 


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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsAristotle University of ThessalonikiGreece

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