Infinite dimensional versions of the Schur-Horn theorem
| 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.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.identifier.uri | https://hdl.handle.net/1794/11575 | |
| 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 |