LuÍs Carvalho

On the relation between S-spectrum and right spectrum

We use the $\mathbb{R}$-linearity of $Iλ-T$ to define $σ(T)$, the right spectrum of a right $\mathbb{H}$-linear operator $T$ in a right quaternionic Hilbert space. We show that $σ(T)$ coincides with the $S$-spectrum $σ_S(T)$.