On the algebra range of an operator on a Hilbert $C^*$-module over compact operators

Let $X$ be a Hilbert $C^*$-module over the $C^*$-algebra $K(H)$ of all compact operators on a complex Hilbert space $H$. Given an orthogonal projection $p \in K(H)$, we describe the set $V^n(A) = \{\langle Ax,x\rangle \,\,:\,\,x\in X,\,\,\langle x,x \rangle =p\}$ for an arbitrary adjointable operator $A\in B(X)$. The relationship between the set $V^n(A)$ and the matricial range of $A$ is established.