Non-commutative Schur-Horn theorems and extended majorization for hermitian matrices
| dc.creator | Massey, Pedro | |
| dc.date | 2007-12-13 | |
| dc.date.accessioned | 2026-07-07T08:49:14Z | |
| dc.date.available | 2026-07-07T08:49:14Z | |
| dc.description | Let $\mathcal A\subseteq \mat$ be a unital $*$-subalgebra of the algebra $\mat$ of all $n\times n$ complex matrices and let $B$ be an hermitian matrix. Let $\U_n(B)$ denote the unitary orbit of $B$ in $\mat$ and let $\mathcal E_\mathcal A$ denote the trace preserving conditional expectation onto $\mathcal A$. We give an spectral characterization of the set $$ \mathcal E_\mathcal A(\U_n(B))=\{\mathcal E_\mathcal A(U^* B U): U\in \mat,\ \text{unitary matrix}\}.$$ We obtain a similar result for the contractive orbit of a positive semi-definite matrix $B$. We then use these results to extend the notions of majorization and submajorization between self-adjoint matrices to spectral relations that come together with extended (non-commutative) Schur-Horn type theorems. | |
| dc.identifier | https://arxiv.org/abs/0712.2246 | |
| dc.identifier | http://arxiv.org/abs/0712.2246 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144223 | |
| dc.subject | Operator Algebras | |
| dc.subject | 15A24; 15A42 | |
| dc.title | Non-commutative Schur-Horn theorems and extended majorization for hermitian matrices | |
| dc.type | text |