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Representation of bilinear forms in non-Archimedean Hilbert space by linear operators. (English) Zbl 1150.47408
Summary: 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 \(A\).

MSC:
47S10 Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
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