We show that the group generated by triangular and diagonal conjugations is dense in A??(Ω2) (in the compact-uniform topology). Moreover, it is shown that any automorphism of Ω2 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)).
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