Mind the GAP: Amenability Constants and Arens Regularity of Fourier Algebras
| dc.contributor.author | Sawatzky, John | |
| dc.date.accessioned | 2023-08-28T14:34:14Z | |
| dc.date.available | 2023-08-28T14:34:14Z | |
| dc.date.issued | 2023-08-28 | |
| dc.date.submitted | 2023-08-07 | |
| dc.description.abstract | This thesis aims to investigate properties of algebras related to the Fourier algebra $A(G)$ and the Fourier-Stieltjes algebra $B(G)$, where $G$ is a locally compact group. For a Banach algebra $\cA$ there are two natural multiplication operations on the double dual $\cA^{**}$ introduced by Arens in 1971, and if these operations agree then the algebra $\cA$ is said to be Arens regular. We study Arens regularity of the closures of $A(G)$ in the multiplier and completely bounded multiplier norms, denoted $A_M(G)$ and $A_{cb}(G)$ respectively. We prove that if a nonzero closed ideal in $A_M(G)$ or $A_{cb}(G)$ is Arens regular then $G$ must be a discrete group. Amenable Banach algebras were first studied by B.E. Johnson in 1972. For an amenable Banach algebra $\cA$ we can consider its amenability constant $AM(\cA) \geq 1$. We are particularly interested in collections of amenable Banach algebras for which there exists a constant $\lambda > 1$ such that the values in the interval $(1,\lambda)$ cannot be attained as amenability constants. If $G$ is a compact group, then the central Fourier algebra is defined as $ZA(G) = ZL^1(G) \cap A(G)$ and endowed with the $A(G)$ norm. We study the amenability constant theory of $ZA(G)$ when $G$ is a finite group. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/19770 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | Abstract Harmonic Analysis | en |
| dc.subject | Functional Analysis | en |
| dc.subject | Fourier Algebra | en |
| dc.subject | Amenability Constants | en |
| dc.title | Mind the GAP: Amenability Constants and Arens Regularity of Fourier Algebras | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Pure Mathematics | en |
| uws-etd.degree.discipline | Pure Mathematics | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | en |
| uws.contributor.advisor | Forrest, Brian | |
| uws.contributor.advisor | Wiersma, Matthew | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |