Level numbers of a bounded linear operator between normed linear spaces and singular value decomposition revisited

Debmalya Sain, Saikat Roy, Ryotaro Tanaka

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
JournalLinear and Multilinear Algebra
DOIs
Publication statusAccepted/In press - 2020

Keywords

  • adjoint operator
  • Birkhoff–James orthogonality
  • Level number
  • singular value decomposition

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