A note on a theorem of James

• Autores: Manuel Valdivia Ureña
• Localización: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM ), ISSN-e 1578-7303, Vol. 105, Nº. 1, 2011, págs. 139-148
• Idioma: inglés
• DOI: 10.1007/s13398-011-0011-0
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• Resumen

  • Let (en)n=1∞ be the unit basis of the Banach space c0. In this paper we prove that, if X is a separable Banach space, there is a closed bounded absolutely convex subset B of c0 which has the following properties: (1) ej ∈ B, j=1,2,...′, and (en)n=1∞ is a monotone shrinking basis of (c0)B. (2) (c0)B has a topological complement Z in ((c0)B)** which is weak*-closed and isometric to X*. (3) The projection from ((c0)B)** onto Z along (c0)B has norm one. © 2011 Springer-Verlag.

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