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James boundaries and σ-fragmented selectors

B. Cascales, M. Muñoz, J. Orihuela (2008)

Studia Mathematica

We study the boundary structure for w*-compact subsets of dual Banach spaces. To be more precise, for a Banach space X, 0 < ϵ < 1 and a subset T of the dual space X* such that ⋃ B(t,ϵ): t ∈ T contains a James boundary for B X * we study different kinds of conditions on T, besides T being countable, which ensure that X * = s p a n T ¯ | | · | | . (SP) We analyze two different non-separable cases where the equality (SP) holds: (a) if J : X 2 B X * is the duality mapping and there exists a σ-fragmented map f: X → X* such that B(f(x),ϵ)...

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