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)) =...
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2010
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/102497 https://ri.conicet.gov.ar/11336/19430 |
| Aporte de: |
| 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. |
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