Integral Equations and Operator Theory

, Volume 37, Issue 4, pp 437–448

Aluthge transforms of operators

  • Il Bong Jung
  • Eungil Ko
  • Carl Pearcy
Article

DOI: 10.1007/BF01192831

Cite this article as:
Bong Jung, I., Ko, E. & Pearcy, C. Integr equ oper theory (2000) 37: 437. doi:10.1007/BF01192831

Abstract

Associated with every operatorT on Hilbert space is its Aluthge transform\(\tilde T\) (defined below). In this note we study various connections betweenT and\(\tilde T\), including relations between various spectra, numerical ranges, and lattices of invariant subspaces. In particular, we show that if\(\tilde T\) has a nontrivial invariant subspace, then so doesT, and we give various applications of our results.

1991 Mathematics Subject Classification

47A1547B20

Copyright information

© Birkhäuser Verlag 2000

Authors and Affiliations

  • Il Bong Jung
    • 1
  • Eungil Ko
    • 2
  • Carl Pearcy
    • 3
  1. 1.Department of MathematicsKyungpook National UniversityTaeguKorea
  2. 2.Department of MathematicsEwha Women's UniversitySeoulKorea
  3. 3.Department of MathematicsTexas A&M UniversityCollege StationUSA