Weyl-von Neumann-Berg theorem for quaternionic operators

Abstract

We prove the Weyl-von Neumann-Berg theorem for right linear operators (not necessarily bounded) in a quaternionic Hilbert space: Let N be a right linear normal (need not be bounded) operator in a quaternionic separable infinite dimensional Hilbert space H. Then for a given ϵ > 0, there exists a compact operator K with K<ϵ and a diagonal operator D on H such that N = D + K.