Let X be a real Banach space. The rectangular constant and some generalisations of it, for, 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, correcting some statements appearing in the literature, and extend to some characterisations of uniformly nonsquare spaces, known only for. We also give a characterisation of two-dimensional spaces with hexagonal norms. Finally, we indicate some new upper estimates concerning and.

Revisiting the rectangular constant in banach spaces

Casini E.;
2021-01-01

Abstract

Let X be a real Banach space. The rectangular constant and some generalisations of it, for, 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, correcting some statements appearing in the literature, and extend to some characterisations of uniformly nonsquare spaces, known only for. We also give a characterisation of two-dimensional spaces with hexagonal norms. Finally, we indicate some new upper estimates concerning and.
2020 Mathematics subject classification; 46B20; 46B45; 46B99; 46C15
Baronti, M.; Casini, E.; Papini, P. L.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2124285
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
social impact