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Quotients of $C\left[ {0,1} \right]$ with separable dual

Quotients of $C\left[ {0,1} \right]$ with separable dual

A necessary and sufficient condition for an operator fromC(K),K compact metric, into a Banach spaceX to be an isomorphism on a subspace ofC(K) isometric toC0(ωω) is given.