Rigidity properties of operator systems and partial order relations in the state space of C*-algebras
| dc.contributor.author | Saikia, Hridoyananda | |
| dc.contributor.examiningcommittee | Martin, Robert (Mathematics) | |
| dc.contributor.examiningcommittee | Zorboska, Nina (Mathematics) | |
| dc.contributor.examiningcommittee | Kennedy, Matthew (University of Waterloo) | |
| dc.contributor.supervisor | Clouâtre, Raphaël | |
| dc.date.accessioned | 2025-03-28T17:10:33Z | |
| dc.date.available | 2025-03-28T17:10:33Z | |
| dc.date.issued | 2025-02-24 | |
| dc.date.submitted | 2025-02-24T17:39:48Z | en_US |
| dc.degree.discipline | Mathematics | |
| dc.degree.level | Doctor of Philosophy (Ph.D.) | |
| dc.description.abstract | Arveson’s hyperrigidity conjecture concerns the unique extension property of *-representations of a C*-algebra with respect to a generating operator system. The maximal states in the dilation order fully encapsulate the cyclic representations of a C*-algebra with the unique extension property. A reformulation of the conjecture by Davidson and Kennedy raises the question whether the maximal measures in the dilation order are concentrated on a particular set. In this thesis, we address this question for general C*-algebras. We show the existence of a projection such that the dilation maximal states are precisely those states which are concentrated on the projection. We also reformulate the conjecture in terms of the non-commutative topological properties of this projection. Choquet order is a partial order defined on the set of regular Borel probability measures on a compact convex set. With the help of two equivalent characterizations of Choquet order, we define strong dilation relation and sub-division relation on the state space of a C*-algebra. The equivalence of the two relations is not known in general. We show that the strong dilation relation is stronger than the sub-division relation. Moreover, we show the equivalence of the strong dilation relation with a non-commutative sub-division relation. We also demonstrate that these relations can serve as valuable tools for investigating certain rigidity properties of a generating operator system of a C*-algebra. | |
| dc.description.note | May 2025 | |
| dc.identifier.uri | http://hdl.handle.net/1993/38970 | |
| dc.language.iso | eng | |
| dc.subject | Operator System | |
| dc.subject | C*-algebra | |
| dc.subject | Hyperrigidity | |
| dc.subject | Dilation | |
| dc.subject | Boundary projection | |
| dc.subject | Choquet order | |
| dc.title | Rigidity properties of operator systems and partial order relations in the state space of C*-algebras | |
| local.subject.manitoba | no |