Complex Analysis and Operator Theory

, Volume 7, Issue 2, pp 409–419 | Cite as

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

  • Zenon Jan Jabłoński
  • Il Bong Jung
  • Jan Stochel
Article

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.

Keywords

Directed tree Weighted shift on a directed tree Formally normal operator Normal operator Subnormal operator 

Mathematics Subject Classification (2010)

Primary 47B15 47B37 Secondary 47B20 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Zenon Jan Jabłoński
    • 1
  • Il Bong Jung
    • 2
  • Jan Stochel
    • 1
  1. 1.Instytut MatematykiUniwersytet JagiellońskiKrakówPoland
  2. 2.Department of MathematicsKyungpook National UniversityDaeguKorea

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