IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Multivariable Schur-Horn theorems
Autor/es:
MOHAN RAVICHANDRAN; PEDRO MASSEY
Revista:
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
Editorial:
LONDON MATH SOC
Referencias:
Lugar: Londres; Año: 2016 vol. 112 p. 206 - 206
ISSN:
0024-6115
Resumen:
We prove a variety of results describing the diagonals of tuples of commuting hermitian operators in type II_1 factors. These results, motivated by work of Arveson and Kadison, are generalizations of the classical Schur?Horn theorem to the infinite-dimensional, multivariable setting. Our description of these possible diagonals uses a natural generalization of the classical notion of majorization. In the special case when both the given tuple and the desired diagonal have finite joint spectrum, our results are complete. When the tuples do not have finite joint spectrum, we are able to prove strong approximate results. Unlike the single variable case, the multivariable case presents several surprises and we point out obstructions to extending our complete description in the finite spectrum case to the general case. We also discuss the problem of characterizing diagonals of commuting tuples in B(H) and give approximate characterizations in this case as well.