Prof. Marcin Bownik, PhD (University of Oregon): The Pythagorean Theorem for Orthogonal Projections |
|
| Startdatum/-zeit: | 21.04.2010 17:15 |
| Enddatum/-zeit: | 21.04.2010 |
Veranstalter: |
|
|---|---|
| Adresse: | Fachbereich Mathematik/ Informatik, Institut für Mathematik Prof. Dr. Gitta Kutyniok Albrechtstr. 28a 49076 Osnabrück |
| Telefon: | 0541 - 969 - 3516 |
| Telefax: | 0541 - 969 - 2770 |
| E-Mail: | kutyniok@uos.de |
| Homepage: | http://www.mathematik.uni-osnabrueck.de/kolloquium.html |
Veranstaltungsort: |
|
| Adresse: | Institut für Mathematik Institut für Mathematik, Geb. 69/ Raum 125 Albrechtstr. 28a, 49076 Osnabrück |
| Karte: | Bei Google Maps anzeigen |
| Beschreibung: | The Pythagorean Theorem should be known to everyone after completing elementary school. However, its generalization for orthogonal projections might not be widely known among professional mathematicians due to the fact that it was proved only a few years ago. This theorem characterizes diagonals of orthogonal projections in Hilbert spaces and it was shown in 2002 by Kadison. For finitely dimensional spaces this result is a consequence of a more general Schur-Horn Theorem characterizing diagonals of Hermitian matrices with prescribed eigenvalues. In the finite dimensional case diagonals of a projection are numbers between 0 and 1 summing up to an integer. However, the infinite dimensional case, though simple in formulation, is a much deeper result. In this talk we shall describe Kadison's theorem and some newer results characterizing diagonals of self-adjoint operators with prescribed spectrum. |
| Kategorie: | Mathematisches Kolloquium |
| Suche weitere Termine: | |
