On non-Archimedean hilbertian spaces |
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Authors: | Albert Kubzdela |
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Institution: | aInstitute of Civil Engineering, Poznan University of Technology, Ul, Piotrowo 5, 61-138 Poznań, Poland |
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Abstract: | We consider a special class of non-Archimedean Banach spaces, called Hilbertian, for which every one-dimensional linear subspace has an orthogonal complement. We prove that all immediate extensions of co, contained in l∞, are Hilbertian. In this way we construct examples of Hilbertian spaces over a non-spherically complete valued field without an orthogonal base. |
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Keywords: | MSC: 46S10 |
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