Diagonalization Modulo Norm Ideals with Lipschitz Estimates

Suppose that (X, d) is a compact metric space and thatμis a regular Borel measure onX. Let Lip(X) denote the collection of Lipschitz functions onX. In this paper, we investigate the problem of simultaneous diagonalization of the multiplication operators {Mf: f∈Lip(X)} onL2(X, μ) modulo norm ideals of compact operators.