Representations of Operator Algebras
| dc.comment.hidden | "[The author retains] the right to include the journal article, in full or in part, in a thesis or dissertation." See: http://www.elsevier.com/wps/find/authorsview.authors/rights | en |
| dc.contributor.author | Fuller, Adam Hanley | |
| dc.date.accessioned | 2012-05-11T17:55:10Z | |
| dc.date.available | 2012-05-11T17:55:10Z | |
| dc.date.issued | 2012-05-11T17:55:10Z | |
| dc.date.submitted | 2012-05-08 | |
| dc.description.abstract | The following thesis is divided into two main chapters. In Chapter 2 we study isometric representations of product systems of correspondences over the semigroup 𝐍ᵏ which are minimal dilations of finite dimensional, fully coisometric representations. We show the existence of a unique minimal cyclic coinvariant subspace for all such representations. The compression of the representation to this subspace is shown to be a complete unitary invariant. For a certain class of graph algebras the nonself-adjoint WOT-closed algebra generated by these representations is shown to contain the projection onto the minimal cyclic coinvariant subspace. This class includes free semigroup algebras. This result extends to a class of higher-rank graph algebras which includes higher-rank graphs with a single vertex. In chapter 3 we move onto semicrossed product algebras. Let 𝒮 be the semigroup 𝒮=Σ𝒮ᵢ, where 𝒮ᵢ is a countable subsemigroup of the additive semigroup 𝐑₊ containing 0. We consider representations of 𝒮 as contractions {Tᵣ }ᵣ on a Hilbert space with the Nica-covariance property: Tᵣ*Tᵤ=TᵤTᵣ* whenever t^s=0. We show that all such representations have a unique minimal isometric Nica-covariant dilation. This result is used to help analyse the nonself-adjoint semicrossed product algebras formed from Nica-covariant representations of the action of 𝒮 on an operator algebra 𝒜 by completely contractive endomorphisms. We conclude by calculating the C*-envelope of the isometric nonself-adjoint semicrossed product algebra (in the sense of Kakariadis and Katsoulis). | en |
| dc.identifier.uri | http://hdl.handle.net/10012/6720 | |
| dc.language.iso | en | en |
| dc.pending | false | en |
| dc.publisher | University of Waterloo | en |
| dc.subject | operator algebras | en |
| dc.subject | operator theory | en |
| dc.subject.program | Pure Mathematics | en |
| dc.title | Representations of Operator Algebras | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Pure Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |