Derivations, multipliers and topological centers of certain Banach algebras related to locally compact groups
| dc.contributor.author | Malekzadeh Varnosfaderani, Davood | |
| dc.contributor.examiningcommittee | Stokke, Ross (Mathematics) Zhang, Yong (Mathematics) Wang, Xikui (Statistics) Spronk, Nico (Pore Mathematics, University of Waterloo) | en_US |
| dc.contributor.supervisor | Ghahramani, Freidoun (Mathematics) | en_US |
| dc.date.accessioned | 2017-06-26T16:49:32Z | |
| dc.date.available | 2017-06-26T16:49:32Z | |
| dc.date.issued | 2017 | |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Doctor of Philosophy (Ph.D.) | en_US |
| dc.description.abstract | We introduce certain Banach algebras related to locally compact groups and study their properties. Speci cally, we prove that L1(G) is an ideal of L1 0(G) if and only if G is compact. We also demonstrate that the left topological centers of L1 0(G) and (M(G) 0) are L1(G) and M(G) respectively. Next, we turn our attention to various derivation and left multiplier problems. Speci cally, we show that for every weak-star continuous derivation D : L1(G) ! L1(G) there is 2 M(G) such that D = ad . We also prove that every derivation from L10 (G) into L1(G) is inner. Next, we focus on weakly compact derivations and left multipliers and show that for every weakly compact derivation D on M(G) there is f 2 L1(G) such that D = adf . We also prove that there exists a non-zero weakly compact derivation on L1(G) ( or L10 (G) for the special case where there is a unique right invariant mean on L1(G) ) if and only if G is a non-abelian compact group. We present necessary and su cient conditions for the existence of non-zero weakly compact left multiplier on L10 (G) . We also show that for the special case where there is a unique right invariant mean on L1(G), every weakly compact derivation D on L1(G) is of the form adh where h is in L1(G). We introduce the concepts of quasi-Arens regularity, quasi topological center and quasiweakly almost periodic functionals and show that 2 QWAP(A) if and only if ad is weakly compact. Finally, for a particular G, we construct a continuous non-weakly compact derivation D : L1(G) ! L1(G) such that D(L1(G)) WAP(G). ii | en_US |
| dc.description.note | October 2017 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/32276 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | Banach algebras | en_US |
| dc.subject | Derivations | en_US |
| dc.subject | Left multipliers | en_US |
| dc.subject | Locally compact groups | en_US |
| dc.subject | Arens products | en_US |
| dc.subject | Topological centers | en_US |
| dc.title | Derivations, multipliers and topological centers of certain Banach algebras related to locally compact groups | en_US |
| dc.type | doctoral thesis | en_US |