On subspaces of c₀ and extension of operators into C(K)-spaces

1999/11/18 by N. J. Kalton, Kalton, N. J.
Mathematics · #46B03 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B03

paper · pdf · doi:10.48550/arxiv.math/9911144

18 pages

arxiv created 1999/11/18 · arxiv updated 2009/11/30

Abstract

Johnson and Zippin recently showed that if X is a weak^*-closed subspace of ℓ₁ and T:X-> C(K) is any bounded operator then T can extended to a bounded operator T:ℓ₁→ C(K). We give a converse result: if X is a subspace of ℓ₁ so that ℓ₁/X has a (UFDD) and every operator T:X -> C(K) can be extended to ℓ₁ then there is an automorphism τ of ℓ₁ so that τ(X) is weak^*-closed. This result is proved by studying subspaces of c₀ and several different characterizations of such subspaces are given.

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