Abstract

We show that the group generated by triangular and diagonal conjugations is dense in $$\mathrm Aut (\Omega _2)$$ (in the compact-uniform topology). Moreover, it is shown that any automorphism of $$\Omega _2$$ is a local holomorphic conjugation (it extends the results from (Rostand, Studia Math 155:207–230, 2003, Thomas, Collect Math 59(3):321–324, 2008)).

Highlights

  • Introduction and statement of the resultLet n denote the spectral ball in Cn2, that is a domain composed of n × n complex matrices whose spectral radius is

  • Recall that we presented in [6] two counterexamples to the question on the description of the group of automorphisms of the spectral ball

  • We focus on them in the sense that we classify all automorphisms of the spectral ball of the form x → u(x)xu(x)−1 ∈, where u ∈ O(, M−1) is such that u(x) is either diagonal or triangular, x ∈

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Summary

Introduction and statement of the result

Let n denote the spectral ball in Cn2 , that is a domain composed of n × n complex matrices whose spectral radius is

Diagonal and triangular conjugations
Density of triangular and diagonal conjugations
Limit of conjugations
Local form of the automorphisms of the spectral unit ball
Full Text
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