Paul Skoufranis, York University
“Majorization in C*-Algebras”
A classical result in matrix theory characterizes the convex hull of the unitary orbit of a self-adjoint matrix using spectral data. The description of these convex hulls has many applications such as characterizing the possible diagonal n-tuples of a self-adjoint matrix based on its eigenvalues. As all of these questions have natural analogues in an arbitrary unital C*- algebra, it is natural to ask whether these results have generalizations.
In this talk, using a notion of majorization against unbounded traces, we characterize the norm-closed convex hulls of the unitary orbits of self-adjoint operators in any unital C*- algebra. Furthermore, for several classes of C*-algebras, such as those satisfying Blackadar’s strict comparison of positive elements, an upper bound for the number of unitary conjugates in a convex combination required to approximate an element in the closed convex hull within a given error is shown to exist. (Joint work with P. Ng and L. Robert.)
MC 5417