An extension of the weighted geometric mean in unital $JB$-algebras

Amir Ghasem Ghazanfari, Somayeh Malekinejad

Let $\mathcal{A}$ be a unital $JB$-algebra and $A,B\in \mathcal{A}$, we extend the weighted geometric mean $A{♯}_{r}B$, from $r\in [0,1]$ to $r\in (-1,0)\cup (1,2)$. We will not…