Open Access
April 2017 New results on Kottman’s constant
Jesús M. F. Castillo, Manuel González, Pier Luigi Papini
Banach J. Math. Anal. 11(2): 348-362 (April 2017). DOI: 10.1215/17358787-0000007X


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.


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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.


Received: 18 December 2015; Accepted: 8 June 2016; Published: April 2017
First available in Project Euclid: 22 February 2017

zbMATH: 1368.46016
MathSciNet: MR3612169
Digital Object Identifier: 10.1215/17358787-0000007X

Primary: 46B20
Secondary: 46B03 , 46B04

Keywords: Banach space , Kottman’s constant , twisted Hilbert spaces

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 2 • April 2017
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