Operators on C[0,1] Preserving Copies of Asymptotic ℓ1 Spaces

Abstract

Given separable Banach spaces X, Y , Z and a bounded linear operator T : X → Y , 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… (More)

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