A study of symmetric points in Banach spaces. Issue 5 (24th March 2022)

• Record Type: Journal Article
• Authors: Sain, Debmalya; Roy, Saikat; Bagchi, Satya; Balestro, Vitor
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 5(2022)
• Page Start: 888
• Page End: 898
• Publication Date: 2022-03-24
• Subjects: Birkhoff-James orthogonality -- left-symmetric point -- right-symmetric point -- polyhedral Banach spaces; Primary 46B20 -- Secondary 52A21; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2020.1749541
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: We completely characterize the left-symmetric points, the right-symmetric points, and the symmetric points in the sense of Birkhoff-James, in a Banach space. We obtain a complete characterization of the left-symmetric (right-symmetric) points in the infinity sum of two Banach spaces, in terms of the left-symmetric (right-symmetric) points of the constituent spaces. As an application of this characterization, we explicitly identify the left-symmetric (right-symmetric) points of some well-known three-dimensional polyhedral Banach spaces.