Weyl-von Neumann-Berg theorem for quaternionic operators

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 $ε>0$ there exists a compact operator $K$ with $\|K\|<ε$ and a diagonal operator $D$ on $H$ such that $N=D+K$.

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