| dc.contributor.author | Yahaghi, Bamdad Reza. | en_US |
| dc.date.accessioned | 2014-10-21T12:37:33Z | |
| dc.date.available | 2002 | |
| dc.date.issued | 2002 | en_US |
| dc.identifier.other | AAINQ75712 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10222/55864 | |
| dc.description | This thesis focuses on reducibility and triangularizability of collections of linear transformations on a vector space over a general field as well as compact operators on a real or complex Banach space. It consists of three parts. | en_US |
| dc.description | In part one, we extend triangularization results due to Levitzki. Kolchin, and others. For a given n > 1, we characterize all fields F such that Burnside's Theorem holds in Mn( F). We consider irreducible semigroups and F-algebras of matrices in Mn(K) with traces in a subfield F. We prove Wedderburn-Artin type theorems for such F-algebras of matrices. We use our main results to generalize some other classical triangularization results, e.g., those due to Guralnick, Kaplansky, McCoy, and others, and present applications in finite dimensions over a general field. We also consider semigroups and F-algebras of compact operators on an arbitrary Banach space and Cp class operators on an arbitrary Hilbert space. We present new proofs of certain classical theorems as well as some new triangularization results in this infinite-dimensional setting. | en_US |
| dc.description | In part two, we show that triangularizability is stable under certain limit operations. This is then used to prove an invariant subspace theorem for certain bounded operators. We also prove that in finite dimensions reducibility remains intact under these limit operations provided the underlying space is complex or it is real with odd dimension. | en_US |
| dc.description | In part three, we are interested in extending the triangularization theory to collections of matrices on division rings. We give a new proof of a well-known Theorem of Levitzki and prove an analogue of one of the main results of part one on division rings. We define the concept of permutability of trace on a collection of matrices over a division ring and prove that under a slight condition on the characteristic of the division ring, every irreducible family on which trace is permutable is commutative. | en_US |
| dc.description | Thesis (Ph.D.)--Dalhousie University (Canada), 2002. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Dalhousie University | en_US |
| dc.publisher | | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | Reducibility results on operator semigroups. | en_US |
| dc.type | text | en_US |
| dc.contributor.degree | Ph.D. | en_US |
