Geodesic
Representation of bilinear forms in non-Archimedean Hilbert space by linear operators
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 695-705.

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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 $A$.
Classification : 46C99, 46S10, 47S10
Keywords: non-Archimedean Hilbert space; non-Archimedean bilinear form; unbounded operator; unbounded bilinear form; bounded bilinear form; self-adjoint operator 
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     title = {Representation of bilinear forms in {non-Archimedean} {Hilbert} space by linear operators},
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Diagana, Toka. Representation of bilinear forms in non-Archimedean Hilbert space by linear operators. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 695-705. http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a13/