| dc.contributor.author | Jahandideh, Mohammad Taghi. | en_US |
| dc.date.accessioned | 2014-10-21T12:35:13Z | |
| dc.date.available | 1997 | |
| dc.date.issued | 1997 | en_US |
| dc.identifier.other | AAINQ24747 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10222/55484 | |
| dc.description | The main results in this thesis are about invariant subspaces of multiplicative semigroups of quasinilpotent positive operators on Banach lattices. | en_US |
| dc.description | There are some known results that guarantee the existence of a non-trivial closed invariant ideal for a quasinilpotent positive operator on certain spaces, for example on $C\sb0(\Omega)$ with $\Omega$ a locally compact Hausdorff space or on a Banach lattice with atoms. Some recent results also guarantee the existence of non-trivial closed invariant ideals for a compact quasinilpotent positive operator on an arbitrary Banach lattice. In fact it is known that given such an operator T, on a real or complex Banach lattice, there is a nontrivial closed ideal which is invariant under all positive operators that commute with T. | en_US |
| dc.description | This thesis deals with invariant ideals for families of positive operators on Banach lattices. In particular it studies ideal-decomposable and ideal-triangularizable semi-groups of positive operators. We show that in certain Banach lattices compactness is not required for the existence of hyperinvariant closed ideals for a quasinilpotent positive operator. We also show that in those Banach lattices a semigroup of quasinilpotent positive operators might be decomposable without imposing any compactness condition. We generalize the fact that the only irreducible $C\sb{p}$-closed subalgebra of $C\sb{p}$ is $C\sb{p}$ itself to extend some recent reducibility results and apply them to derive some decomposability theorems concerning a collection of quasinilpotent positive operators on reflexive Banach lattices. | en_US |
| dc.description | We use these results for "ideal-triangularization", i.e., we construct a maximal closed ideal chain, each of whose members is invariant under a certain collection of operators that are related to compact positive operators, or to quasinilpotent positive operators. | en_US |
| dc.description | Thesis (Ph.D.)--Dalhousie University (Canada), 1997. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Dalhousie University | en_US |
| dc.publisher | | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | Decomposability and triangularizability of positive operators on Banach lattices. | en_US |
| dc.type | text | en_US |
| dc.contributor.degree | Ph.D. | en_US |
