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Some applications of projective resolutions of identity. (English) Zbl 0798.46008

Summary: We show that the unit ball \(K\) of the bidual of an Asplund space is a Corson compact or contains \([0,\omega_ 1]\), and that it has the Namioka property on separate-to-joint continuity. The same results are shown for \(K\) a Valdivia compact; a by-product is that all dyadic compacts have the Namioka property. Some connections with weakly compactly generated dual spaces and renormings are given.

MSC:

46B20 Geometry and structure of normed linear spaces
46B03 Isomorphic theory (including renorming) of Banach spaces
54D30 Compactness
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