Geodesic
Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 3, pp. 431-442.

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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.
Classification : 46S10, 47A07, 47S10
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 
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Attimu, Dodzi; Diagana, Toka. Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 3, pp. 431-442. http://geodesic.mathdoc.fr/item/CMUC_2007__48_3_a4/