Amenability Properties of Banach Algebra of Banach Algebra-Valued Continuous Functions
| dc.contributor.author | Ghamarshoushtari, Reza | |
| dc.contributor.examiningcommittee | Stokke, Ross (Mathematics) Thulasiraman, Parimala (Computer Science) | en_US |
| dc.contributor.supervisor | Zhang, Yong (Mathematics) | en_US |
| dc.date.accessioned | 2014-04-01T23:10:05Z | |
| dc.date.available | 2014-04-01T23:10:05Z | |
| dc.date.issued | 2014-04-01 | |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| dc.description.abstract | In this thesis we discuss amenability properties of the Banach algebra-valued continuous functions on a compact Hausdorff space X. Let A be a Banach algebra. The space of A-valued continuous functions on X, denoted by C(X,A), form a new Banach algebra. We show that C(X,A) has a bounded approximate diagonal (i.e. it is amenable) if and only if A has a bounded approximate diagonal. We also show that if A has a compactly central approximate diagonal then C(X,A) has a compact approximate diagonal. We note that, unlike C(X), in general C(X,A) is not a C*-algebra, and is no longer commutative if A is not so. Our method is inspired by a work of M. Abtahi and Y. Zhang. In addition to the above investigation, we directly construct a bounded approximate diagonal for C0(X), the Banach algebra of the closure of compactly supported continuous functions on a locally compact Hausdorff space X. | en_US |
| dc.description.note | May 2014 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/23354 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | amenability | en_US |
| dc.subject | Banach algebra-valued functions | en_US |
| dc.subject | pseudo-amenability | en_US |
| dc.subject | compactly-invariant approximate diagonal | en_US |
| dc.title | Amenability Properties of Banach Algebra of Banach Algebra-Valued Continuous Functions | en_US |
| dc.type | master thesis | en_US |