Two-parameter super-product systems of compact Hausdorff spaces

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dc.contributor.advisorFloricel, Remus
dc.contributor.authorMelanson, Patrick
dc.contributor.committeememberArgerami, Martín
dc.contributor.externalexaminerZilles, Sandra
dc.date.accessioned2023-12-18T18:04:10Z
dc.date.available2023-12-18T18:04:10Z
dc.date.issued2023-06
dc.descriptionA Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics, University of Regina. iv, 56 p.
dc.description.abstractThe theory of C∗−algebras [1, 7,17] is incredibly rich and provides a great starting point for exploring various types of operator algebras within the realm of Functional Analysis. Previous papers [8, 12] have used these algebras to analyze what are called C∗-product systems and C∗-subproduct systems, as a natural generalization of two parameter product systems of Hilbert spaces, introduced by B. Tsirelson in [18]. The Gelfand duality shows that commutative unital C∗-product and subproduct systems are directly related to certain two-parameter families of compact Hausdorff spaces, referred to in this paper as compact super-product systems. Building on this, we define the concept of flattening and show that each compact super-product system can be flattened through a projective limit construction. Furthermore, we are able to define a one-parameter “multiplication” induced by this flattening, which behaves well within the framework of a C∗-product system. Finally, we show that these results hold when considering the appropriate measures for these spaces, as well as the various constructions defined within them.
dc.description.authorstatusStudenten
dc.description.peerreviewyesen
dc.identifier.tcnumberTC-SRU-16197
dc.identifier.thesisurlhttps://ourspace.uregina.ca/bitstreams/4e62e9ed-84be-4f04-abea-3b4cdc9fb0ae/download
dc.identifier.urihttps://hdl.handle.net/10294/16197
dc.language.isoenen
dc.publisherFaculty of Graduate Studies and Research, University of Reginaen
dc.titleTwo-parameter super-product systems of compact Hausdorff spaces
dc.typeThesisen
thesis.degree.departmentDepartment of Mathematics and Statistics
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Reginaen
thesis.degree.levelMaster'sen
thesis.degree.nameMaster of Science (MSc)
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