## Osaka Journal of Mathematics

### Rank-one Perturbation of Weighted Shifts on a Directed Tree: Partial Normality and Weak Hyponormality

#### Abstract

A special rank-one perturbation $S_{t,n}$ of a weighted shift on a directed tree is constructed. Partial normality and weak hyponormality (including quasinormality, $p$-hyponormality, $p$-paranormality, absolute-$p$-paranormality and $A(p)$-class) of $S_{t,n}$ are characterized.

#### Article information

Source
Osaka J. Math., Volume 55, Number 3 (2018), 439-462.

Dates
First available in Project Euclid: 4 July 2018

https://projecteuclid.org/euclid.ojm/1530691237

Mathematical Reviews number (MathSciNet)
MR3824840

Zentralblatt MATH identifier
06927821

#### Citation

R. Exner, George; Jung, Il Bong; Lee, Eun Young; Seo, Minjung. Rank-one Perturbation of Weighted Shifts on a Directed Tree: Partial Normality and Weak Hyponormality. Osaka J. Math. 55 (2018), no. 3, 439--462. https://projecteuclid.org/euclid.ojm/1530691237

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