Square roots of semihyponormal operators have scalar extensions

✍ Scribed by Eungil Ko

• Publisher: Elsevier Science
• Year: 2003
• Tongue: French
• Weight: 108 KB
• Volume: 127
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/s0007-4497(03)00040-x

✦ Synopsis

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 Colojoarȃ-Foiaş). As a corollary, we obtain that an operator T ∈ ( √ SH ) has a nontrivial invariant subspace if its spectrum has interior in the plane.