Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n×n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give a spectral characterization of the set EA(Un(B)) =...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/19430 |
| Acceso en línea: | http://hdl.handle.net/11336/19430 |
| Access Level: | acceso abierto |
| Palabra clave: | Extended majorization non-commutative Schur-Horn theorems diagonal block compressions partial traces unitary orbit https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n×n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give a spectral characterization of the set EA(Un(B)) = {EA(U ∗B U) : U ∈ Mn(C), 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. |
|---|