Takeshi Miura

Ring isomorphisms in norm between Banach algebras of continuous functions

Let $X$ and $Y$ be locally compact Hausdorff spaces and let $\mathbb{K}\in \{\mathbb{R},\mathbb{C}\}$. We say that a bijection $T\colon C_0(X,\mathbb{K})\to C_0(Y,\mathbb{K})$ is a ring isomorphism in norm if \[ \|T(f+g)\|=\|T(f)+T(g)\|,\qquad \|T(fg)\|=\|T(f)T(g)\| \] for every $f,g\in C_0(X,\mathbb{K})$. We determine...