Homotopy of vector states

Esteban Andruchow, Alejandro Varela

Let $B$ be a C${}^{\ast }$-algebra and $X$ a C${}^{\ast }$ Hilbert $B$-module. If $p\in B$ is a projection, denote by $S_p=\{x\in X:<x,x>=p\}$, the $p$-sphere of $X$. For $\varphi$ a state of $B$ w…