Complex Analysis and Operator Theory

, Volume 7, Issue 2, pp 409–419

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

  • Zenon Jan Jabłoński
  • Il Bong Jung
  • Jan Stochel

DOI: 10.1007/s11785-011-0177-7

Cite this article as:
Jabłoński, Z.J., Jung, I.B. & Stochel, J. Complex Anal. Oper. Theory (2013) 7: 409. doi:10.1007/s11785-011-0177-7


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.


Directed treeWeighted shift on a directed treeFormally normal operatorNormal operatorSubnormal operator

Mathematics Subject Classification (2010)

Primary 47B1547B37Secondary 47B20

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