A class of weighted Bergman spaces, reducing subspaces for multiple weighted shifts, and dilatable operators

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dc.contributor.authorLiang, Xiaomingen
dc.contributor.committeechairOlin, Robert F.en
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberParry, Charles J.en
dc.contributor.committeememberThomson, James E.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:17:45Zen
dc.date.adate2006-08-14en
dc.date.available2014-03-14T21:17:45Zen
dc.date.issued1996-08-15en
dc.date.rdate2006-08-14en
dc.date.sdate2006-08-14en
dc.description.abstractThis thesis consists of four chapters. Chapter 1 contains the preliminaries. We give the background, notation and some results needed for this work, and we describe our main results of this thesis. In Chapter 2 we will introduce a class of weighted Bergman spaces. We then will discuss some properties about the multiplication operator, Mz , on them. We also characterize the dual spaces of these weighted Bergman spaces. In Chapter 3 we will characterize the reducing subspaces of multiple weighted shifts. The reducing subspaces of the Bergman and the Dirichlet shift of multiplicity N are portrayed from this characterization. In Chapter 4 we will introduce the class of super-isometrically dilatable operators and describe their elementary properties. We then will discuss an equivalent description of the invariant subspace lattice for the Bergman shift. We will also discuss the interpolating sequences on the bidisk. Finally, we will examine a special class of super-isometrically dilatable operators. One corollary of this work is that we will prove that the compression of the Bergman shift on two compliments of two invariant subspaces are unitarily equivalent if and only if the two invariant subspaces are equal.en
dc.description.degreePh. D.en
dc.format.extentiv, 78 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-08142006-110124en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-08142006-110124/en
dc.identifier.urihttp://hdl.handle.net/10919/39164en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1996.L536.pdfen
dc.relation.isformatofOCLC# 35798910en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectWeighted Shiften
dc.subjectReducing Subspaceen
dc.subjectInvariant Subspaceen
dc.subjectSuper-Dilatable Operatoren
dc.subject.lccLD5655.V856 1996.L536en
dc.titleA class of weighted Bergman spaces, reducing subspaces for multiple weighted shifts, and dilatable operatorsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en
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