Monotone unitary families
| dc.creator | Grieser, Daniel | |
| dc.date | 2007-11-19 | |
| dc.date.accessioned | 2026-07-07T08:43:42Z | |
| dc.date.available | 2026-07-07T08:43:42Z | |
| dc.description | A unitary family is a family of unitary operators $U(x)$ acting on a finite dimensional hermitian vector space, depending analytically on a real parameter $x$. It is monotone if $\frac1i U'(x)U(x)^{-1}$ is a positive operator for each $x$. We prove a number of results generalizing standard theorems on the spectral theory of a single unitary operator $U_0$, which correspond to the 'commutative' case $U(x)=e^{ix}U_0$. Also, for a two-parameter unitary family -- for which there is no analytic perturbation theory -- we prove an implicit function type theorem for the spectral data under the assumption that the family is monotone in one argument. | |
| dc.description | 9 pages; extended version of what was the appendix to arXiv:0710.3405 v1 | |
| dc.identifier | https://arxiv.org/abs/0711.2869 | |
| dc.identifier | http://arxiv.org/abs/0711.2869 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142408 | |
| dc.subject | Functional Analysis | |
| dc.subject | Spectral Theory | |
| dc.subject | 47A55 | |
| dc.title | Monotone unitary families | |
| dc.type | text |