The Weyl-Von Neumann Theorem for Multipliers Of Some Af-Algebras

Abstract

A well known theorem of Weyl-von Neumann asserts that if X is a self-adjoint operator acting on a separable Hilbert space, then there is a decomposition 1 = Σ en of the identity into finite rank projections so that we may write X = Σ ƛnen + y, where the ƛnare scalars and y is a compact operator with small norm. In other words, X can be approximately diagonalized.