Browsing Mathematics Theses and Dissertations by Author "Jasper, John, 1981"
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Jasper, John, 1981 (University of Oregon, June , 2011)[more][less]Jasper, John, 1981 20110927T22:05:12Z 20110927T22:05:12Z 201106 http://hdl.handle.net/1794/11575 ix, 99 p. We characterize the diagonals of four classes of selfadjoint operators on infinite dimensional Hilbert spaces. These results are motivated by the classical SchurHorn theorem, which characterizes the diagonals of selfadjoint matrices on finite dimensional Hilbert spaces. In Chapters II and III we present some known results. First, we generalize the SchurHorn 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 SchurHorn 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 SchurHorn 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 coauthored material. Committee in charge: Marcin Bownik, Chair; N. Christopher Phillips, Member; Yuan Xu, Member; David Levin, Member; Dietrich Belitz, Outside Member en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2011; Mathematics Pure sciences SchurHorn theorem Diagonals Frames Selfadjoint operators Infinite dimensional versions of the SchurHorn theorem Thesis
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