Abstract: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.
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
AMS Subject Classification: 47S10, 46S10