Topics in the notion of operator amenability and its generalizations with application in Fourier algebras
| dc.contributor.author | makareh shireh, miad | |
| dc.contributor.examiningcommittee | Zhang, Yong (Mahematics) Xikui, Wang (Statistics) Stokke, Ross (Mathematics, University of Winnipeg) Lykova, Zinaida (Newcastle University) | en_US |
| dc.contributor.supervisor | Ghahramani, Fereidoun (Mathematics) | en_US |
| dc.date.accessioned | 2019-04-26T18:26:46Z | |
| dc.date.available | 2019-04-26T18:26:46Z | |
| dc.date.issued | 2019-01-21 | en_US |
| dc.date.submitted | 2019-04-26T17:37:49Z | en |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Doctor of Philosophy (Ph.D.) | en_US |
| dc.description.abstract | The operator algebraists have for a long time realized the significance of studying matrices of elements of an operator algebra in order for obtaining results about the algebra. This lead Z. J. Ruan, D. Blecher and others to introduce the notion of an abstract operator space in late 1980’s. Ruan, furthermore, introduced the notion of completely contractive Banach algebras and operator-space amenability for such algebras. He showed that the Fourier algebra A(G) of a locally compact group G is operator-space amenable if and only if the group G is amenable. In this thesis we investigate further the notion of operator-space amenability and its approximate versions. In particular for the Fourier algebras. We also prove results on perturbation theory of these notions. Furthermore we study the question of when A⊗ˆB ( or A⊗γ B) is (approximately) operatorspace (or weakly) amenable what conclusions can one derive about the components. | en_US |
| dc.description.note | May 2019 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/33875 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | Operator amenability, Fourier algebras | en_US |
| dc.title | Topics in the notion of operator amenability and its generalizations with application in Fourier algebras | en_US |
| dc.type | doctoral thesis | en_US |