| dc.contributor.author | Simonic, Aleksander. | en_US |
| dc.date.accessioned | 2014-10-21T12:35:05Z | |
| dc.date.available | 1995 | |
| dc.date.issued | 1995 | en_US |
| dc.identifier.other | AAINN05227 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10222/55042 | |
| dc.description | The existence of invariant subspaces for bounded linear operators acting on an infinite dimensional Hilbert space appears to be one of the most difficult questions in the theory of linear transformations. The question is known as the invariant subspace problem. Very few affirmative answers are known regarding this problem. One of the most prominent ones is the theorem on the existence of hyper invariant subspaces for compact operators due to V. I. Lomonosov. | en_US |
| dc.description | The aim of this work is to generalize Lomonosov's technique in order to apply them to a wider class of not necessarily compact operators. We start by establishing a connection between the existence of invariant subspaces and density of what we define as the associated Lomonosov space in a certain function space. On a Hilbert space approximation with Lomonosov functions results in an extended version of Burnside's theorem. An application of this theorem to the algebra generated by an essentially self-adjoint operator A yields the existence of vector states on the space of all polynomials restricted to the essential spectrum of A. Finally, the invariant subspace problem for compact perturbations of self-adjoint operators is translated into an extreme problem and the solution is obtained upon differentiating certain real-valued functions at their extreme. | en_US |
| dc.description | The invariant subspace theorem for essentially self-adjoint operators acting on an infinite-dimensional real Hilbert space is the main result of this work and represents an extension of the known techniques in the theory of invariant subspaces. | en_US |
| dc.description | Thesis (Ph.D.)--Dalhousie University (Canada), 1995. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Dalhousie University | en_US |
| dc.publisher | | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | An extension of Lomonosov's techniques to non-compact operators. | en_US |
| dc.type | text | en_US |
| dc.contributor.degree | Ph.D. | en_US |
