Multiplicative bijections of semigroups of interval-valued continuous functions

Abstract

We characterize all compact and Hausdorff spaces $X$ which satisfy that for every multiplicative bijection $\varphi$ on $C(X,I)$, there exist a homeomorphism $\mu :X\to X$ and a continuous map $p:X\to (0,+\infty )$ such that $$\varphi (f)(x)=f(\mu (x){)}^{p(x)}$$ for every $f\in C(X,I)$ and $x\in X$. This allows us to disprove a conjecture of Marovt (Proc. Amer. Math. Soc. {\bf 134} (2006), 1065-1075). Some related results on other semigroups of functions are also given.

9 pages. No figures. Accepted for publication

References in corpus (1)

• Sequential isomorphisms between the sets of von Neumann algebra effects