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dc.contributor.authorBindner, Donald J
dc.date.accessioned2014-03-03T20:03:02Z
dc.date.available2014-03-03T20:03:02Z
dc.date.issued2001-12
dc.identifier.otherbindner_donald_j_200112_phd
dc.identifier.urihttp://purl.galileo.usg.edu/uga_etd/bindner_donald_j_200112_phd
dc.identifier.urihttp://hdl.handle.net/10724/20284
dc.description.abstractIn this work, the re exivity properties of the space spanned by the powers of an operator and its adjoint are investigated. For an operator A, let T A be the weak-star closure of f A j ; (A ) j j j 0 g . Call A star-re exive if T A is re exive and star-transitive if T A is transitive. |The regular unilateral shift is known to be star-transitive, as are the unicel- lular shifts. We will discover that many non-injective weighted shifts are not star- transitive, but rather star-re exive. Among the operators found to be star-re exive are direct sums of non-nilpotent shifts, 0 T for injective shifts T where T has a nonzero eigenvalue, and A A where A is a Jordan matrix. |There is an explicit construction of a star-re exive weighted shift T similar to the regular unilateral shift S. This contrasts distinctly with the star-transitive nature of S. The similarity that carries S to T is of the simplest type, a diagonal matrix. This example illustrates clearly that the property of being star-re exive is not invariant under similarity. |The question of similarity and star-re exivity is also explored for n n matrices. It is shown that Mn contains an open dense set of matrices that are both re exive and star-transitive. It is also shown, for n 4, that the only star-re exive, complex- valued matrices in Mn with n distinct eigenvalues are normal matrices.
dc.publisheruga
dc.rightspublic
dc.subjectOperator theory
dc.subjectUnilateral shift
dc.subjectWeighted shift
dc.subjectReflexive
dc.subjectTransitive
dc.subjectDirect sum
dc.subjectWeak-star topology.
dc.titleOn the space spanned by the powers of an operator and its adjoint
dc.typeDissertation
dc.description.degreePhD
dc.description.departmentMathematics
dc.description.majorMathematics
dc.description.advisorEdward A. Azoff
dc.description.committeeEdward A. Azoff
dc.description.committeeElliot C. Gootman
dc.description.committeeElham Izadi
dc.description.committeeRobert Varley
dc.description.committeeShuzhou Wang


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