Osaka Journal of Mathematics

On operators which are power similar to hyponormal operators

Sungeun Jung, Eungil Ko, and Mee-Jung Lee

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Abstract

In this paper, we study power similarity of operators. In particular, we show that if $T \in \mathit{PS}(H)$ (defined below) for some hyponormal operator $H$, then $T$ is subscalar. From this result, we obtain that such an operator with rich spectrum has a nontrivial invariant subspace. Moreover, we consider invariant and hyperinvariant subspaces for $T \in \mathit{PS}(H)$.

Article information

Source
Osaka J. Math., Volume 52, Number 3 (2015), 833-849.

Dates
First available in Project Euclid: 17 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1437137620

Mathematical Reviews number (MathSciNet)
MR3370477

Zentralblatt MATH identifier
1323.47022

Subjects
Primary: 47A11: Local spectral properties
Secondary: 47A15: Invariant subspaces [See also 47A46] 47B20: Subnormal operators, hyponormal operators, etc.

Citation

Jung, Sungeun; Ko, Eungil; Lee, Mee-Jung. On operators which are power similar to hyponormal operators. Osaka J. Math. 52 (2015), no. 3, 833--849. https://projecteuclid.org/euclid.ojm/1437137620


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