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Positivity

, Volume 7, Issue 3, pp 195–202 | Cite as

Operator Semigroups for which Reducibility Implies Decomposability

  • L. Livshits
  • G. Macdonald
  • B. Mathes
  • H. Radjavi
Article
  • 48 Downloads

Abstract

A description of the lattice of invariant subspaces is provided for multiplicative semigroups \(\mathcal{S}\) of bounded operators on Lp(X,μ) which are closed under multiplication on the left or right by bounded multiplication operators. Applications are then given to semigroups of positive quasinilpotent operators.

decomposable positive operator quasinilpotent reducible semigroup 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • L. Livshits
    • 1
  • G. Macdonald
    • 2
  • B. Mathes
    • 1
  • H. Radjavi
    • 3
  1. 1.Department of MathematicsColby CollegeWatervilleUSA
  2. 2.Department of Math and CSUniversity of Prince Edward IslandCharlottetownCanada
  3. 3.Department of Math, Stats and CSDalhousie UniversityHalifaxCanada

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