Weak Hamburger-type weighted shifts and their examples

Exner, George R.; Jin, Joo Young; Jung, Il Bong; Lee, Eun Ji

doi:10.1016/j.jmaa.2018.02.045

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“…An operator T in L(H) is said to be weakly n-hyponormal if p(T) is hyponormal for any polynomial p with degree less than or equal to n. An operator T is polynomially hyponormal if p(T) is hyponormal for every polynomial p. In particular, the weak two-hyponormality (or weak three-hyponormality) is referred to as quadratical hyponormality (or cubical hyponormality, resp.) and has been considered in detail in [1][2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights

Ryoo

2019

Mathematics

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Section: Introductionmentioning

confidence: 99%

On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights

Ryoo

2019

Mathematics

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Hamburger-type weighted shifts: Jumping flatness and Aluthge transforms

Exner

Jin

Jung

et al. 2021

Journal of Mathematical Analysis and Applications

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Weakly n-hyponormal weighted shifts: A sufficient condition and their examples

Baek,

Lee,

2023

Filomat

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The n-hyponormal and weakly n-hyponormal weighted shifts were developed to study bridges of operators between the subnormal and hyponormal operators on an infinite dimensional complex Hilbert space about 30 years ago. In this paper we discuss the distinction between the classes of n-hyponormal and weakly n-hyponormal weighted shifts. For such a purpose we consider an arbitrary contractive hyponormal weighted shift W? and find a sufficient condition for the weak n-hyponormality of W?. We provide a general technique for distinction between the n-hyponormality and the weak n-hyponormality of W?, and investigate the distinction between the classes of n-hyponormal and weakly n-hyponormal weighted shifts with Bergman shift and some other examples.

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Weak Hamburger-type weighted shifts and their examples

Cited by 3 publications

References 12 publications

On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights

On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights

Hamburger-type weighted shifts: Jumping flatness and Aluthge transforms

Weakly n-hyponormal weighted shifts: A sufficient condition and their examples

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