Square roots of semihyponormal operators have scalar extensions

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In this paper, we study some properties of (SH), i.e., square roots of semihyponormal operators. In particular we show that an operator T∈(SH) has a scalar extension, i.e., is similar to the restriction to an invariant subspace of a (generalized) scalar operator (in the sense of Colojoara-Foiaş). As a corollary, we obtain that an operator T∈(SH) has a nontrivial invariant subspace if its spectrum has interior in the plane.

Original languageEnglish
Pages (from-to)557-567
Number of pages11
JournalBulletin des Sciences Mathematiques
Issue number6
StatePublished - Aug 2003

Bibliographical note

Funding Information:
E-mail address: eiko@ewha.ac.kr (E. Ko). 1 The author is supported by the KOSEF Research Project No. R01-2000-00003.


  • Invariant subspace
  • Property (β)
  • Semihyponormality
  • Subscalarity


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