Osaka Journal of Mathematics

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

George R. Exner, Il Bong Jung, Eun Young Lee, and Minjung Seo

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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

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1530691237

Mathematical Reviews number (MathSciNet)
MR3824840

Zentralblatt MATH identifier
06927821

Subjects
Primary: 47B20: Subnormal operators, hyponormal operators, etc. 05C20: Directed graphs (digraphs), tournaments 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Secondary: 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 47A50: Equations and inequalities involving linear operators, with vector unknowns

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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