The paper considers representing symmetric, non-degenerate, bilinear forms on some non-Archimedean Hilbert spaces by linear operators. Namely, upon making some assumptions it will be shown that if $\phi$ is a symmetric, non-degenerate bilinear form on a non-Archimedean Hilbert space, then $\phi$ is representable by a unique self-adjoint (possibly unbounded) operator $A$.

The paper considers the representation of non-degenerate bilinear forms on the non-Archimedean Hilbert space ${𝔼}_{\omega }\times {𝔼}_{\omega }$ by linear operators. More precisely, upon making some suitable assumptions we prove that if $\varphi$ is a non-degenerate bilinear form on ${𝔼}_{\omega }\times {𝔼}_{\omega }$, then $\varphi$ is representable by a unique linear operator $A$ whose adjoint operator $A^{*}$ exists.