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New results on Kottman's constant

Abstract: We present new results on Kottman's constant of a Banach space, showing (i) that every Banach space is isometric to a hyperplane of a Banach space having Kottman's constant 2 and (ii) that Kottman's constant of a Banach space and of its bidual can be di erent. We say that a Banach space is a Diestel space if the in mum of Kottman's constants of its subspaces is greater that 1. We show that every Banach space contains a Diestel subspace and that minimal Banach spaces are Diestel spaces.

 Fuente: Banach Journal of Mathematical Analysis, 2017, 11(2), 348-362

 Editorial: Duke University Press

 Año de publicación: 2017

 Nº de páginas: 15

 Tipo de publicación: Artículo de Revista

 DOI: 10.1215/17358787-0000007X

 ISSN: 1735-8787,2662-2033

 Proyecto español: MTM2013-45643

Autoría

CASTILLO, JESÚS M. F.

PAPINI, PIER LUIGI