Weyl-von Neumann-Berg theorem for quaternionic operators

Abstract

We prove the Weyl-von Neumann-Berg theorem for quaternionic 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 Hilbert space $H$. Then for a given $\epsilon >0$ there exists a compact operator $K$ with $\Vert K\Vert <\epsilon$ and a diagonal operator $D$ on $H$ such that $N=D+K$.

9 pages; submitted to a journal

References in corpus (1)

• Continuous slice functional calculus in quaternionic Hilbert spaces