Distance between unitary orbits of normal elements

Ruofei Wang   (East China Normal University)

14:00-15:00,April 13,2023   A503


It is an interesting and important problem to determine when two normal elements are unitary equivalent in a C*-algebra. Let dist(U(x),U(y)) denote the distance between the unitary orbits of x and y. For matrices Mn, let x,y Mn be two normal elements with eigenvalues {_1,...,_n} and {_1,...,_n} respectively. Suppose (x,y) = min_ max_(1in)|_i - _(i)|, where runs over all permutations of {1,...,n}. The equality dist(U(x),U(y)) = (x,y) for Hermitian matrices and the inequality dist(U(x),U(y)) (x,y) for normal matrices are well known by Weyl (1912). This stimulates more research. Recently, S. Hu and H. Lin (2015) studied the distance between unitary orbits in separable simple C*-algebras of real rank zero and stable rank one with important results. Some results about distance between unitary orbits of normal elements would be introduced in the talk.

About the speaker: