Structure of Invariant Subspaces for Left-Invertible Operators on Hilbert Space

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dc.contributor.authorSutton, Daniel Josephen
dc.contributor.committeechairBall, Joseph A.en
dc.contributor.committeememberSun, Shu-Mingen
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberJohnson, Martin E.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:15:44Zen
dc.date.adate2010-09-15en
dc.date.available2014-03-14T20:15:44Zen
dc.date.issued2010-08-12en
dc.date.rdate2010-09-15en
dc.date.sdate2010-08-26en
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 $l^1$, 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.en
dc.description.degreePh. D.en
dc.identifier.otheretd-08262010-161822en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-08262010-161822/en
dc.identifier.urihttp://hdl.handle.net/10919/28807en
dc.publisherVirginia Techen
dc.relation.haspartSutton_DJ_D_2010.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectIndexen
dc.subjectWandering Subspaceen
dc.subjectInvariant Subspaceen
dc.subjectWeighted Shiften
dc.subjectLeft-Invertibleen
dc.titleStructure of Invariant Subspaces for Left-Invertible Operators on Hilbert Spaceen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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