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Johnson and Zippin recently showed that if  X  is a weak * ‐closed subspace of ℓ 1  and  T  :  X  →  C ( K ) is any bounded operator then  T  can be extended to a bounded operator  T̃  : ℓ 1  →  C ( K ). We give a converse result: if X  is a subspace of ℓ 1  such that ℓ 1 / X  has an unconditional finite‐dimensional decomposition (UFDD) and every operator  T  :  X  →  C ( K ) can be extended to ℓ 1  then there is an automorphism τ of ℓ 1  such that τ( X ) is weak * ‐closed. This result is proved by studying subspaces of  c  0  and several different characterizations of such subspaces are given.

On Subspaces of c 0 and Extension of Operators into C ( K )‐Spaces