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

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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 preserves a copy of C([0,1]).

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  1. Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

    I. Gasparis

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Gasparis, I. Operators on C[0,1] preserving copies of asymptotic ℓ1 spaces. Math. Ann. 333, 831–858 (2005). https://doi.org/10.1007/s00208-005-0702-y

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