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2-Variable weighted shifts and recursiveness: toral Aluthge transform and subnormality

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Abstract

In this paper, we aim to study the Toral Aluthge transform of 2-variable weighted shifts, whose moments sequence satisfies a bi-indexed linear recursive relation of Fibonacci type. In addition, some related subnormal properties for the Toral Aluthge transform of this class of 2-variable weighted shifts are explored. Illustrative examples and applications are provided.

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References

  1. Ben Taher, R., and M. Rachidi. 2017. Truncated moment problems in \({\mathbb{R}}^2 \)and recursiveness. Operators and Matrices 11 (4): 953–968.

    Article  MathSciNet  Google Scholar 

  2. Ben Taher, R., and M. Rachidi. 2016. Solving some generalized Vandermonde systems and inverse of their associate matrices via new approaches for the Binet formula. Applied Mathematics and Computation 290: 267–280.

    Article  MathSciNet  Google Scholar 

  3. Bentaher, R., M. Rachidi, and E.H. Zerouali. 2015. On the Aluthge Transforms of Weighted Shifts with Moments of Fibonacci Tyoe. Application to Subnormality, Integral Equations and Operator Theory 82 (2): 287–299.

    Article  Google Scholar 

  4. Curto, R.E., J. Kim, and J. Yoon. 2019. The Aluthge transform of unilateral weighted shifts and the Square Root Problem for finitely atomic measures. Mathematische Nachrichten 292: 2352–2368.

    Article  MathSciNet  Google Scholar 

  5. Curto, R.E., and J. Yoon. 2018. Aluthge transforms of 2-variable weighted shifts. Integral Equations and Operator Theory 90: 90:52.

    Article  MathSciNet  Google Scholar 

  6. Curto, R.E., and L.A. Fialkow. 1993. Recursively generated weighted shifts and the subnormal completion. Integral Equations and Operator Theory 17: 202–246.

    Article  MathSciNet  Google Scholar 

  7. Halmos, P.R. 1950. Normal dilations and extensions of operators. Summa Brasiliensis Mathematicae 2: 125–134.

    MathSciNet  Google Scholar 

  8. Lee, S.H., W.Y. Lee, and J. Yoon. 2012. Subnormality of Aluthge transforms of weighted shifts. Integral Equations and Operator Theory 72 (2): 241–251.

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors express their sincere thanks to the referee for his/here valuable review and significants comments. The useful suggestions and observations of Prof. Raúl Curto, allow us to improved the content of this paper, we would like to express our sincere gratitude to him. The second author expresses his sincere thanks to the UFMS and the INMA for their valuable support. He also thanks his colleagues of the UFMS for their encouragements, in particular Profs N. F. de Almeida, P. Sandalo, E. Pereira and Magda Junqueira Gudinho Mongelli.

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Authors and Affiliations

  1. Equip EDA - Département de Mathématiques, Faculté des Sciences, Université Moulay Ismail, B.P. 4010, Beni M’hamed, Meknes, Morocco

    Rajae Ben Taher

  2. Institute of Mathematics - INMA, Federal University of Mato Grosso do Sul - UFMS, Campo Grande, MS, 79070-900, Brazil

    Mustapha Rachidi

Authors
  1. Rajae Ben Taher
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  2. Mustapha Rachidi
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Correspondence to Rajae Ben Taher.

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This study has not received any research funding. The authors declare that there is no conflict of interest.

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Ben Taher, R., Rachidi, M. 2-Variable weighted shifts and recursiveness: toral Aluthge transform and subnormality. J Anal 28, 1107–1126 (2020). https://doi.org/10.1007/s41478-020-00239-9

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  • DOI: https://doi.org/10.1007/s41478-020-00239-9

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