On the relation between S-spectrum and right spectrum

LuÍs Carvalho; Cristina Diogo; Sérgio Mendes; Helena Soares

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arXiv · 2303.05335

On the relation between S-spectrum and right spectrum

LuÍs Carvalho·Cristina Diogo·Sérgio Mendes·Helena Soares

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Abstract

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

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LuÍs Carvalho, Cristina Diogo, Sérgio Mendes, Helena Soares. 2023-03-09. On the relation between S-spectrum and right spectrum. https://arxiv.org/abs/2303.05335

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