m at h . FA ] 1 4 O ct 1 99 6 A counterexample to a question of
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چکیده
We give an example of a compact metric space K, an open dense subset U of K, and a sequence (fn) in C(K) which is pointwise convergent to a non-continuous function on K, such that for every u ∈ U there exists n ∈ N with fn(u) = fm(u) for all m ≥ n, yet (fn) is equivalent to the unit vector basis of the James quasi-reflexive space of order 1. Thus c0 does not embed isomorphically in the closed linear span [fn] of (fn). This answers in negative a question asked by H. Haydon, E. Odell and H. Rosenthal.
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