On the definition of Hilbert space |
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Authors: | Herbert H Gross Hans A Keller |
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Institution: | 1. In der Halden 2, CH-8603, Schwerzenbach 2. Haldenstrasse 8, CH-9400, Rorschach
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Abstract: | The projection theorem expresses a central feature of classical Hilbert space. Do other infinite dimensional sesquilinear spaces share this property? We show here that this is not the case for several prominent candidates; in particular Kalish's p-adic Hilbert spaces, Springers non archimedean normed spaces, the positive definite spaces over ordered fields. This yields interesting characterizations of classical Hilbert space. |
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