Commutativity and orthogonality of similarity orbits in Banach algebras

Muhammad Hassen, Rudi Brits, Francois Schulz

For a semisimple unital Banach algebra $A$ over $\mathbb{C}$, and elements $a,b\in A,$ we show that the similarity orbits, $\mathrm{orb}(a)$ and $\mathrm{orb}(b)$, over the princip…