Distance between unitary orbits of normal elements

Ruofei Wang 王若飞  (East China Normal University)

14:00-15:00,April 13,2023   A503

Abstract:

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 {α_1,...,α_n} and {β_1,...,β_n} respectively. Suppose δ(x,y) = min_π max_(1≤i≤n)|α_i - β_π(i)|, where π runs over all permutations of {1,...,n}. The equality dist(U(x),U(y)) = δ(x,y) for Hermitian matrices and the inequality dist(U(x),U(y)) ≤ δ(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.

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