A canonical decomposition for linear operators and linear relations

S. Hassi*, Z. Sebestyén, H.S.V. de Snoo, F.H. Szafraniec

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    37 Citations (Scopus)
    9 Downloads (Pure)

    Abstract

    An arbitrary linear relation (multivalued operator) acting from one Hilbert space to another Hilbert space is shown to be the sum of a closable operator and a singular relation whose closure is the Cartesian product of closed subspaces. This decomposition can be seen as an analog of the Lebesgue decomposition of a measure into a regular part and a singular part. The two parts of a relation are characterized metrically and in terms of Stone's characteristic projection onto the closure of the linear relation.
    Original languageEnglish
    Pages (from-to)281-307
    Number of pages27
    JournalActa mathematica hungarica
    Volume115
    Issue number4
    DOIs
    Publication statusPublished - Jun-2007

    Keywords

    • relation
    • multivalued operator
    • graph
    • adjoint relation
    • closable operator
    • regular relation
    • singular relation
    • Stone decomposition
    • LEBESGUE-TYPE DECOMPOSITION
    • POSITIVE OPERATORS
    • ADJOINT OPERATORS
    • HILBERT-SPACE
    • RANGES

    Fingerprint

    Dive into the research topics of 'A canonical decomposition for linear operators and linear relations'. Together they form a unique fingerprint.

    Cite this