Distance between unitary orbits of normal elements
Ruofei Wang ÍõÈô·É (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 ¡Ê Mn be two normal elements with eigenvalues
{¦Á_1,...,¦Á_n} and {¦Â_1,...,¦Â_n} respectively. Suppose
¦Ä(x,y) = min_¦Ð
max_(1¡Üi¡Ün)|¦Á_i - ¦Â_¦Ð(i)|,
where ¦Ð runs over all permutations of {1,...,n}. The equality dist(U(x),U(y)) = ¦Ä(x,y)
for Hermitian matrices and the inequality dist(U(x),U(y)) ¡Ü ¦Ä(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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