The local form of doubly stochastic maps and joint majorization in II_1 factors

MARTIN ARGERAMI; PEDRO MASSEY

INTEGRAL EQUATIONS AND OPERATOR THEORY

Birkhauser Verlag Basel

Año: 2008 vol. 61 p. 1 - 19

0378-620X

We find a description of the restriction of doubly stochastic maps to separable abelian C*-subalgebras of a II_1 factor 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 II_1 factor case. Several characterizations of this joint majorization are obtained. As a byproduct we prove that any separable abelian C*-subalgebra of M can be embedded into a separable abelian C*-subalgebra of M with diffuse spectral measure.