Abstract
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 language | English |
|---|---|
| Pages (from-to) | 557-567 |
| Number of pages | 11 |
| Journal | Bulletin des Sciences Mathematiques |
| Volume | 127 |
| Issue number | 6 |
| DOIs | |
| State | Published - Aug 2003 |
Bibliographical note
Funding Information:E-mail address: [email protected] (E. Ko). 1 The author is supported by the KOSEF Research Project No. R01-2000-00003.
Keywords
- Invariant subspace
- Property (β)
- Semihyponormality
- Subscalarity