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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
Zbl 1150.47408
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