Virginia Tech
Structure of Invariant Subspaces for Left-Invertible Operators on Hilbert Space
Abstract
dc:description.abstractThis dissertation is primarily concerned with studying the invariant subspaces of left-invertible, weighted shifts, with generalizations to left-invertible operators where applicable. The two main problems that are researched can be stated together as When does a weighted shift have the one-dimensional wandering subspace property for all of its closed, invariant subspaces? This can fail either by having a subspace that is not generated by its wandering subspace, or by having a subspace with an index greater than one. For the former we show that every left-invertible, weighted shift is similar to another weighted shift with a residual space, with respect to being generated by the wandering subspace, of dimension $n$, where $n$ is any finite number. For the latter we derive necessary and sufficient conditions for a pure, left-invertible operator with an index of one to have a closed, invariant subspace with an index greater than one. We use these conditions to show that if a closed, invariant subspace for an operator in a class of weighted shifts has a vector in l1, then it must have an index equal to one, and to produce closed, invariant subspaces with an index of two for operators in another class of weighted shifts.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2010
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Sutton, Daniel Joseph
- Chair dc:contributor.committeechair
-
- Ball, Joseph A.
- Committee members dc:contributor.committeemember
-
- Sun, Shu-Ming
- Klaus, Martin
- Johnson, Martin E.
Subjects
dc:subject × 5Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-08262010-161822
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/28807