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 different. We say that a Banach space is a Diestel space if the infimum 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.
Citation
Jesús M. F. Castillo. Manuel González. Pier Luigi Papini. "New results on Kottman’s constant." Banach J. Math. Anal. 11 (2) 348 - 362, April 2017. https://doi.org/10.1215/17358787-0000007X
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