A contractive version of a Schur-Horn theorem in \(\mathrm{II}_{1}\) factors. (English) Zbl 1130.46038
Summary: We prove a contractive version of the Schur-Horn theorem for submajorization in II\(_{1}\) factors that complements some previous results on the Schur-Horn theorem within this context. We obtain a reformulation of a conjecture of W. Arveson and R. V. Kadison [Contemp. Math. 414, 247–263 (2006; Zbl 1113.46064)] regarding a strong version of the Schur-Horn theorem in \(\text{II}_{1}\) factors in terms of submajorization and contractive orbits of positive operators.
MSC:
| 46L35 | Classifications of \(C^*\)-algebras |
| 47A30 | Norms (inequalities, more than one norm, etc.) of linear operators |
| 15A42 | Inequalities involving eigenvalues and eigenvectors |
| 15A45 | Miscellaneous inequalities involving matrices |
| 52A05 | Convex sets without dimension restrictions (aspects of convex geometry) |
Citations:
Zbl 1113.46064References:
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