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Representation of bilinear forms in non-Archimedean Hilbert space by linear operators. II. (English) Zbl 1199.47334
Summary: The paper considers the representation of nondegenerate bilinear forms on the non-Archimedean Hilbert space \(\mathbb E_\omega \times \mathbb E_\omega \) by linear operators. More precisely, under some suitable assumptions, we prove that, if \(\varphi \) is a nondegenerate bilinear form on \(\mathbb E_\omega \times \mathbb E_\omega \), then \(\varphi \) is representable by a unique linear operator \(A\) whose adjoint operator \(A^*\) exists.
[For Part I, see ibid. 47, No. 4, 695–705 (2006; Zbl 1150.47408).]
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
Citations:
Zbl 1150.47408
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