Lebesgue type decompositions and Radon–Nikodym derivatives for pairs of bounded linear operators

Seppo Hassi*, Henk De Snoo

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
32 Downloads (Pure)

Abstract

For a pair of bounded linear Hilbert space operators A and Bone considers the Lebesgue type decompositions of B with respect toA into an almost dominated part and a singular part, analogous to theLebesgue decomposition for a pair of measures in which case one speaks ofan absolutely continuous and a singular part. A complete parametrizationof all Lebesgue type decompositions will be given, and the uniqueness ofsuch decompositions will be characterized. In addition, it will be shownthat the almost dominated part of B in a Lebesgue type decomposition hasan abstract Radon–Nikodym derivative with respect to the operator A.

Original languageEnglish
Pages (from-to)469-503
Number of pages35
JournalActa scientiarum mathematicarum
Volume88
Issue number1-2
DOIs
Publication statusPublished - Aug-2022

Keywords

  • 46N30
  • 47A05
  • 47A06
  • 47A65
  • 47N30
  • almost dominated part
  • Lebesgue type decompositions
  • operator range
  • pair of bounded operators
  • Radon–Nikodym derivative
  • singular part

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