# Article

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Keywords:
non-Archimedean Hilbert space; bilinear form; continuous linear functionals; non-Archimedean Riesz theorem; bounded bilinear form; stable unbounded bilinear form; unstable unbounded bilinear form
Summary:
The paper considers the representation of non-degenerate bilinear forms on the non-Archimedean Hilbert space $\Bbb E_\omega \times \Bbb E_\omega$ by linear operators. More precisely, upon making some suitable assumptions we prove that if $\varphi$ is a non-degenerate bilinear form on $\Bbb E_\omega \times \Bbb E_\omega$, then $\varphi$ is representable by a unique linear operator $A$ whose adjoint operator $A^*$ exists.
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