, Volume 7, Issue 2, pp 409-419
Date: 12 Aug 2011

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.

Communicated by Guest Editors L. Littlejohn and J. Stochel.
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).
Dedicated to Professor Franciszek H. Szafraniec on the occasion of his 70th birthday.