2007/12/13 by Pedro Massey, Massey, Pedro
Computer Science · Mathematics · #15A24 #15A42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.0712.2246
openalex publication_date 2007/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathcal A⊆ \mat be a unital *-subalgebra of the algebra \mat of all n× n complex matrices and let B be an hermitian matrix. Let \Un(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(\Un(B))=\\mathcal E_\mathcal A(U^* B U): U∈ \mat, 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.