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Unbounded Norm Convergence in Banach Lattices

  • Author / Creator
    O'Brien, Michael J
  • In this thesis we describe basic properties of unbounded norm convergence (un-convergence) and investigate its relationship with other convergences in Banach lattices. In particular, we show that in order continuous Banach lattices with a weak unit, un-convergence can be viewed as a generalization of convergence in measure. We also obtain several useful facts about the relationship of un-convergence with unbounded order convergence.

  • Subjects / Keywords
  • Graduation date
    2016-06
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3QZ22P0K
  • 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.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Troitsky, Vladimir (Department of Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Schmuland, Byron (Department of Mathematical and Statistical Sciences)
    • Tcaciuc, Adi (Department of Mathematics at MacEwan University)
    • Dai, Feng (Department of Mathematical and Statistical Sciences)