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Distances to spaces of affine Baire-one functions

Jiří Spurný (2010)

Studia Mathematica

Let E be a Banach space and let ( B E * ) and ( B E * ) denote the space of all Baire-one and affine Baire-one functions on the dual unit ball B E * , respectively. We show that there exists a separable L₁-predual E such that there is no quantitative relation between d i s t ( f , ( B E * ) ) and d i s t ( f , ( B E * ) ) , where f is an affine function on B E * . If the Banach space E satisfies some additional assumption, we prove the existence of some such dependence.

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