Abstract
The Hardy spaces Hp(X) of holomorphic functions on the unit discDin the complex plane with values in a complex Banach space X are studied. For an arbitrary X and 0<p<1, a representation of the continuous linear functionals on Hp(X) is obtained. It is proved that if 0<p<1 and X does not have the Analytic Radon Nikodym Property, then the space of all X-valued polynomials is not dense but is weakly dense in Hp(X). Moreover, if X contains a copy of c0 then Hp(X) does not have the Orlicz-Pettis property.
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