Irreducible Operators and Semigroups on Banach Lattices

• Author / Creator

  Gao, Niushan

• In this thesis, I study irreducibility on Banach lattices. First, I study irreducible positive operators on Banach lattices. I develop a uniform approach to several comparison theorems of positive operators. I also use a comparison theorem to show that if one of the two semi-commuting positive operators is compact then their commutator is quasinilpotent. Second, I study irreducible semigroups of positive operators on arbitrary Banach lattices. An extension of Perron-Frobenius theory is established and applied to improve some classical results. Third, I study compact positive operators K with irreducible super right or left commutants (which are always semigroups). I prove that every operator semi-commuting with K commutes with K. I also prove that the restriction of K to its peripheral spectral subspace is a permutation.

• Subjects / Keywords

  • Irreducible operators
  • Irreducible semigroups

• Graduation date

  Fall 2013

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R36395

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.