Let $H$ be a complex Hilbert space, ${\cal B}(H)$ be the set of bounded
linear operator on $H$, ${\cal E}(H)$ be the set of $\{A\in {\cal B}(H): 0\leq
A\leq I\}$, $1\leq n\leq\infty$, ${\cal A}=\{E_i\}_{i=1}^{n}\subseteq {\cal
E}(H)$ be commutative, $\Phi_{{\cal A}}$ be the completely positive map which
be defined by $\Phi_{{\cal A}}:{\cal B}(H)\longrightarrow {\cal B}(H):
B\longmapsto \sum\limits_n A_n B A_n^*$. In this paper, we prove the following
results:

(1). If $\sum_{i=1}^{n}E_i^2=I$ in strong operator topology, then the fixed
points set ${\cal B}(H)^{\Phi_{{\cal A}}}$ of $\Phi_{{\cal A}}$ is ${\cal A}'$,
that is $${\cal B}(H)^{\Phi_{\mathcal{A}}}=\{B\in {\cal
B}(H)|\Phi_{\mathcal{A}}(B)= \sum\limits_{i=1}^{n}E_iB E_i=B\}=\mathcal {A}'.$$

(2). If $F=\sum_{i=1}^{n}E_i^2<I$, then the fixed points set ${\cal
B}(H)^{\Phi_{{\cal A}}}$ of $\Phi_{{\cal A}}$ is $P^F(\{1\})\mathcal {A}'$,
where $P^F$ is the spectral measure of $F$, that is $${\cal
B}(H)^{\Phi_{\mathcal{A}}}=\{B\in {\cal B}(H)|\Phi_{\mathcal{A}}(B)=
\sum\limits_{i=1}^{n}E_iB E_i=B\}=P^F(\{1\})\mathcal {A}'.$$