Level numbers of a bounded linear operator between normed linear spaces and singular value decomposition revisited. Issue 19 (16th December 2022)

• Record Type: Journal Article
• Authors: Sain, Debmalya; Roy, Saikat; Tanaka, Ryotaro
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 19(2022)
• Page Start: 3905
• Page End: 3922
• Publication Date: 2022-12-16
• Subjects: Level number -- Birkhoff–James orthogonality -- adjoint operator -- singular value decomposition; Primary 47L05 -- Secondary 15A18; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2020.1857677
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: We introduce the notion of level numbers of a bounded linear operator between normed linear spaces, as a generalization of the singular values of an operator between inner product spaces. We study the geometric and the analytic properties of the level numbers, in connection with Birkhoff–James orthogonality and norm optimization problems. We also illustrate the similarities and the differences between the level numbers and the singular values of an operator. As an application of the present study, we obtain a new and elementary approach to the singular value decomposition of matrices.