dc.contributor.author |
Jasper, John, 1981- |
|
dc.date.accessioned |
2011-09-27T22:05:12Z |
|
dc.date.available |
2011-09-27T22:05:12Z |
|
dc.date.issued |
2011-06 |
|
dc.identifier.uri |
http://hdl.handle.net/1794/11575 |
|
dc.description |
ix, 99 p. |
en_US |
dc.description.abstract |
We characterize the diagonals of four classes of self-adjoint operators on infinite dimensional Hilbert spaces. These results are motivated by the classical Schur-Horn theorem, which characterizes the diagonals of self-adjoint matrices on finite dimensional Hilbert spaces.
In Chapters II and III we present some known results. First, we generalize the Schur-Horn theorem to finite rank operators. Next, we state Kadison's theorem, which gives a simple necessary and sufficient condition for a sequence to be the diagonal of a projection. We present a new constructive proof of the sufficiency direction of Kadison's theorem, which is referred to as the Carpenter's Theorem.
Our first original Schur-Horn type theorem is presented in Chapter IV. We look at operators with three points in the spectrum and obtain a characterization of the diagonals analogous to Kadison's result.
In the final two chapters we investigate a Schur-Horn type problem motivated by a problem in frame theory. In Chapter V we look at the connection between frames and diagonals of locally invertible operators. Finally, in Chapter VI we give a characterization of the diagonals of locally invertible operators, which in turn gives a characterization of the sequences which arise as the norms of frames with specified frame bounds.
This dissertation includes previously published co-authored material. |
en_US |
dc.description.sponsorship |
Committee in charge: Marcin Bownik, Chair;
N. Christopher Phillips, Member;
Yuan Xu, Member;
David Levin, Member;
Dietrich Belitz, Outside Member |
en_US |
dc.language.iso |
en_US |
en_US |
dc.publisher |
University of Oregon |
en_US |
dc.relation.ispartofseries |
University of Oregon theses, Dept. of Mathematics, Ph. D., 2011; |
|
dc.subject |
Mathematics |
en_US |
dc.subject |
Pure sciences |
en_US |
dc.subject |
Schur-Horn theorem |
en_US |
dc.subject |
Diagonals |
en_US |
dc.subject |
Frames |
en_US |
dc.subject |
Self-adjoint operators |
en_US |
dc.title |
Infinite dimensional versions of the Schur-Horn theorem |
en_US |
dc.type |
Thesis |
en_US |