Topologies on PositiveType Functions on Groupoids, Weak Containment of Continuous Unitary Representations, and Property (T)

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dc.contributor.advisorWillett, Rufus
dc.contributor.authorCorea, Kenneth
dc.contributor.departmentMathematics
dc.date.accessioned2022-10-19T22:36:26Z
dc.date.available2022-10-19T22:36:26Z
dc.date.issued2022
dc.description.degreePh.D.
dc.identifier.urihttps://hdl.handle.net/10125/103942
dc.subjectMathematics
dc.subjectcontinuous representations
dc.subjectgroupoids
dc.subjectproperty (T)
dc.subjectweak containment
dc.titleTopologies on PositiveType Functions on Groupoids, Weak Containment of Continuous Unitary Representations, and Property (T)
dc.typeThesis
dcterms.abstractWe introduce two new topologies on the space of normalized positive type functions on a groupoid with Haar system, the weak* topology and fiberwise compact convergence topology. We demonstrate these topologies are equivalent when the groupoid is second countable and locally compact, thereby extending Raikov's theorem. Using the fiberwise compact convergence topology we introduce a notion of weak contaiment of continuous unitary representations of a groupoid. We characterize weak containment of the trivial representation with almost invariant sections which extends the idea of almost invariant vectors in group representations. This weak containment naturally suggests a definition of property (T) for groupoids which extends Kazhdan's group property (T). We briefly explore this property and attempt to generalize some of the classic results from the theory of groups.
dcterms.extent44 pages
dcterms.languageen
dcterms.publisherUniversity of Hawai'i at Manoa
dcterms.rightsAll UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.
dcterms.typeText
local.identifier.alturihttp://dissertations.umi.com/hawii:11523

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