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REVISITING THE RECTANGULAR CONSTANT IN BANACH SPACES
Published online by Cambridge University Press: 26 April 2021
Abstract
Let X be a real Banach space. The rectangular constant
$\mu (X)$
and some generalisations of it,
$\mu _p(X)$
for
$p \geq 1$
, were introduced by Gastinel and Joly around half a century ago. In this paper we make precise some characterisations of inner product spaces by using
$\mu _p(X)$
, correcting some statements appearing in the literature, and extend to
$\mu _p(X)$
some characterisations of uniformly nonsquare spaces, known only for
$\mu (X)$
. We also give a characterisation of two-dimensional spaces with hexagonal norms. Finally, we indicate some new upper estimates concerning
$\mu (l_p)$
and
$\mu _p(l_p)$
.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 124 - 133
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © Australian Mathematical Publishing Association Inc. 2021
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