Diagonalization and Unitary Equivalence Modulo Schatten p-Classes
by
Jingbo Xia
State University of New York at Buffalo

We give a necessary and sufficient condition for a commuting tuple A = (A₁, ..., A_n) of self-adjoint operators to be simultaneously diagonalizable modulo the Schatten class C_p, 1 < p < \infty. This condition leads to a classification modulo unitary equivalence and C_p for such tuples which have no isolated eigenvalues of finite multiplicity.

Date received: May 4, 1999