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Normal Extensions Escape from the Class of Weighted Shifts on Directed Trees

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Abstract

A formally normal weighted shift on a directed tree is shown to be a bounded normal operator. The question of whether a normal extension of a subnormal weighted shift on a directed tree can be modeled as a weighted shift on some, possibly different, directed tree is answered.

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Authors and Affiliations

  1. Instytut Matematyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, 30348, Kraków, Poland

    Zenon Jan Jabłoński & Jan Stochel

  2. Department of Mathematics, Kyungpook National University, Daegu, 702-701, Korea

    Il Bong Jung

Authors
  1. Zenon Jan Jabłoński
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  2. Il Bong Jung
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  3. Jan Stochel
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Corresponding author

Correspondence to Zenon Jan Jabłoński.

Additional information

Communicated by Guest Editors L. Littlejohn and J. Stochel.

Dedicated to Professor Franciszek H. Szafraniec on the occasion of his 70th birthday.

Research of Z.J. Jabłoński and J. Stochel was supported by the MNiSzW (Ministry of Science and Higher Education) Grant NN201 546438 (2010–2013). I.B. Jung was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0087565).

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Jabłoński, Z.J., Jung, I.B. & Stochel, J. Normal Extensions Escape from the Class of Weighted Shifts on Directed Trees. Complex Anal. Oper. Theory 7, 409–419 (2013). https://doi.org/10.1007/s11785-011-0177-7

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  • DOI: https://doi.org/10.1007/s11785-011-0177-7

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