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Permanent link (DOI): https://doi.org/10.7939/R3QZ22P0K

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Unbounded Norm Convergence in Banach Lattices Open Access

Descriptions

Other title
Subject/Keyword
Unbounded norm convergence
Banach lattices
Convergence in measure
Un-topology
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
O'Brien, Michael J
Supervisor and department
Troitsky, Vladimir (Department of Mathematical and Statistical Sciences)
Examining committee member and department
Schmuland, Byron (Department of Mathematical and Statistical Sciences)
Dai, Feng (Department of Mathematical and Statistical Sciences)
Tcaciuc, Adi (Department of Mathematics at MacEwan University)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2016-09-22T10:46:49Z
Graduation date
2016-06:Fall 2016
Degree
Master of Science
Degree level
Master's
Abstract
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.
Language
English
DOI
doi:10.7939/R3QZ22P0K
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. 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.
Citation for previous publication
Y. Deng, M. O'Brien and V.G. Troitsky, Unbounded norm convergence in Banach lattices, submitted.

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