What does Birkhoff--James orthogonality know about the norm?

Ljiljana Arambašić                <meta name=

2023/102/1-2 (13) — DOI: 10.5486/PMD.2023.9388 — pp. 197-218

What does Birkhoff—James orthogonality know about the norm?

Authors: Ljiljana Arambašić, Alexander Guterman, Bojan Kuzma, Rajna Rajić and Svetlana Zhilina

Abstract:

It is shown that Birkhoff—James orthogonality knows everything about the smooth norms in reflexive Banach spaces and can also compute the dimensions of the underlying normed spaces.

Keywords: normed vector space, Birkhoff—James orthogonality, graph, diameter, clique

Mathematics Subject Classification: 46B20, 05C20