On the relation between S-spectrum and right spectrum

LuÍs Carvalho; Cristina Diogo; Sérgio Mendes; Helena Soares

On the relation between S-spectrum and right spectrum

Functional Analysis 2023-03-10 v1

Authors: LuÍs Carvalho , Cristina Diogo , Sérgio Mendes , Helena Soares

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 $\sigma_S(T)$ .

Keywords

numerical range spectral theory

Cite

@article{arxiv.2303.05335,
  title  = {On the relation between S-spectrum and right spectrum},
  author = {LuÍs Carvalho and Cristina Diogo and Sérgio Mendes and Helena Soares},
  journal= {arXiv preprint arXiv:2303.05335},
  year   = {2023}
}

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