Multiplicatively spectrum-preserving and norm-preserving maps between invertible groups of commutative Banach algebras

Osamu Hatori, Takeshi Miura, Hiroyuki Takaggi

Let $A$ and $B$ be unital semisimple commutative Banach algebras and $T$ a map from the invertible group $A^{-1}$ onto $B^{-1}$. Linearity and multiplicativity of the map are not a…