Does Stinespring's dilation theorem hold if the algebra of interest is a topological $\ast$-algebra instead of the usual $C^{\ast}$-algebra?

I will now state the version of Stinespring's dilation theorem that I know, and am wondering what happens if I were to replace the $C^{\ast}$-algebra with a topological $\ast$-algebra.

**Theorem.** Let $\mathfrak{A}$ be a unital $C^{\ast}$-algebra, and let $\Phi : \mathfrak{A} \to \mathcal{B}(\mathcal{H})$ be a completely positive map. Then there exists a Hilbert space $\hat{\mathcal{H}}$, a unital $\ast$-homomorphism $\pi : \mathfrak{A} \to \mathcal{B}(\hat{\mathcal{H}})$ and a bounded operator $V : \mathcal{H} \to \hat{\mathcal{H}}$ with $||\Phi(1_{\mathfrak{A}})||=||V||^{2}$ such that
\begin{equation}
\Phi (a)= V^{*} \pi (a) V, \; \; \; \; \; a \in \mathfrak{A}.
\end{equation}

**Notation.** Let $1_{\mathfrak{A}}$ denote the unit in $\mathfrak{A}.$

References to literature on the subject would be greatly appreciated as well.

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