The Local Form of Doubly Stochastic Maps and Joint Majorization in II 1 Factors

Article

Abstract.

We find a description of the restriction of doubly stochastic maps to separable abelian C*-subalgebras of a II 1 factor \({\mathcal{M}}\). We use this local form of doubly stochastic maps to develop a notion of joint majorization between n-tuples of mutually commuting self-adjoint operators that extends those of Kamei (for single self-adjoint operators) and Hiai (for single normal operators) in the II1 factor case. Several characterizations of this joint majorization are obtained. As a byproduct we prove that any separable abelian C*-subalgebra of \({\mathcal{M}}\) can be embedded into a separable abelian C*-subalgebra of \({\mathcal{M}}\) with diffuse spectral measure.

Mathematics Subject Classification (2000).

Primary 46L51 Secondary 46L10 

Keywords.

Joint majorization doubly stochastic map convex hull unitary orbit 

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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of ReginaSaskatchewanCanada
  2. 2.Departamento de Matemática, Facultad de Ciencias ExactasUniversidad Nacional de La PlataLa PlataArgentina

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