Logarithmic submajorization, uniform majorization and Hölder type inequalities for τ-measurable operators

P. G. Dodds, T. K. Dodds, F. A. Sukochev, D. Zanin

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We extend the notion of the determinant function Λ, originally introduced by T.Fack for τ-compact operators, to a natural algebra of τ-measurable operators affiliated with a semifinite von Neumann algebra which coincides with that defined by Haagerup and Schultz in the finite case and on which the determinant function is shown to be submultiplicative. Application is given to Hölder type inequalities via general Araki–Lieb–Thirring inequalities due to Kosaki and Han and to a Weyl-type theorem for uniform majorization.

Original languageEnglish
Pages (from-to)809-830
Number of pages22
JournalIndagationes Mathematicae
Volume31
Issue number5
DOIs
Publication statusPublished - Sep 2020

Keywords

  • Fuglede–Kadison theorem
  • Logarithmic submajorization
  • Measurable operators
  • Semifinite von Neumann algebra
  • Uniform majorization

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