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ISSN 1088-6850(e) ISSN 0002-9947(p)

Baire classes of Banach spaces and strongly affine functions

Author(s): Jirí Spurny
Journal: Trans. Amer. Math. Soc. 362 (2010), 1659-1680.
MSC (2000): Primary 46A55; Secondary 26A21
Posted: October 20, 2009
MathSciNet review: 2563744
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Abstract: We construct a metrizable simplex and a Baire-two function on satisfying the barycentric formula such that is not of affine class two; i.e., there is no bounded sequence of affine Baire-one functions on converging to . This provides an example of a Banach $\mathcal{L}_\infty$ -space such that $E_{2}^{**}\neq E_{\mathcal{B}_2}^{**}$ .

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