Hamburger-type weighted shifts: Jumping flatness and Aluthge transforms

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

doi:10.1016/j.jmaa.2020.124592

Cited by 3 publications

(6 citation statements)

References 14 publications

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“…1. Theorem 2.4 together with [2,Corollary 4.11] shed some light on questions (HP) and (SP) in [9] concerning the preservation of subnormality and Hamburger type property by the Aluthge transform of weighted shifts.…”

Section: Weighted Shifts With Subnormal Aluthge Transformmentioning

confidence: 99%

“…For the last point, since the measure ν is Hamburger determinate we get that the Aluthge transform is subnormal if and only if ν is supported on R + . Sufficiency is obtained by [9,Theorem 5.7].…”

Section: Weighted Shifts With Subnormal Aluthge Transformmentioning

confidence: 99%

“…Recall the following definitions from [9], For a large familly of shifts, a flatness phenomena occurs, when two successive weight are equal. More precisely Proposition 1.2.…”

Section: Introductionmentioning

confidence: 99%

“…In several recent papers, the problem of subnormatiy of the aluthge transform of weighted shifts was considered. See [9], for example. In [9], the next question sas considered (HP) Under what conditions is the Hamburger-type property of a weighted shift preserved under the Aluthge transform?…”

Section: Introductionmentioning

confidence: 99%

“…See [9], for example. In [9], the next question sas considered (HP) Under what conditions is the Hamburger-type property of a weighted shift preserved under the Aluthge transform?…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Jumping flatness and Aluthge transform of recursive weighted shifts

Azhar¹,

Idrissi²,

Zerouali³

2020

Preprint

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We devote this paper to Hamburger type weighted shifts. We give in particular an affirmative answer to a problem concerning subnormality of the Aluthge transform of Hamburger moment measures with finite support. we also extend the notion flatness, "jumping flatness property" introduced recently by Exner et all for Hamburger-type weighted shift and provide obtain several results related to the representing measure of such weighted shifts.

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Section: Weighted Shifts With Subnormal Aluthge Transformmentioning

confidence: 99%

Section: Weighted Shifts With Subnormal Aluthge Transformmentioning

confidence: 99%

“…Recall the following definitions from [9], For a large familly of shifts, a flatness phenomena occurs, when two successive weight are equal. More precisely Proposition 1.2.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…See [9], for example. In [9], the next question sas considered (HP) Under what conditions is the Hamburger-type property of a weighted shift preserved under the Aluthge transform?…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Jumping flatness and Aluthge transform of recursive weighted shifts

Azhar¹,

Idrissi²,

Zerouali³

2020

Preprint

View full text Add to dashboard Cite

show abstract

Jumping flatness and Aluthge transform of recursive weighted shifts

Azhar

Idrissi

Zerouali

2023

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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Hamburger-type weighted shifts: Jumping flatness and Aluthge transforms

Cited by 3 publications

References 14 publications

Jumping flatness and Aluthge transform of recursive weighted shifts

Jumping flatness and Aluthge transform of recursive weighted shifts

Jumping flatness and Aluthge transform of recursive weighted shifts

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

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