Banach Journal of Mathematical Analysis

New results on Kottman’s constant

Jesús M. F. Castillo, Manuel González, and Pier Luigi Papini

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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.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 2 (2017), 348-362.

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1487732418

Digital Object Identifier
doi:10.1215/17358787-0000007X

Mathematical Reviews number (MathSciNet)
MR3612169

Zentralblatt MATH identifier
1368.46016

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46B03: Isomorphic theory (including renorming) of Banach spaces 46B04: Isometric theory of Banach spaces

Keywords
Kottman’s constant Banach space twisted Hilbert spaces

Citation

Castillo, Jesús M. F.; González, Manuel; Papini, Pier Luigi. New results on Kottman’s constant. Banach J. Math. Anal. 11 (2017), no. 2, 348--362. doi:10.1215/17358787-0000007X. https://projecteuclid.org/euclid.bjma/1487732418


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