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Let (H?)b be the Bourgain algebra of HOO c LI?. We prove (H?)b = HI + C. In particular if f E LI then the Hankel operator Hf is a compact map of HOO into BMO iff whenever f, -0 weakly in HI?, then dist(ffn, HOO) , O .

Completely continuous Hankel operators on $H\sp \infty$ and Bourgain algebras