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Smoothness in weakly compactly generated Banach spaces

1983; Elsevier BV; Volume: 52; Issue: 3 Linguagem: Inglês

10.1016/0022-1236(83)90073-3

1096-0783

Gilles Godefroy, Stanimir Troyanski, J. H. Whitfield, Václav Zizler,

Advanced Harmonic Analysis Research

If X∗ is a weakly compactly generated (WCG) Banach space, then X admits an equivalent C1-smooth norm. If a WCG Banach space X admits a Ck-smooth function with bounded support, then X admits Ck-smooth partitions of unity.