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On a valuation field invented by A. Robinson and certain structures connected with it

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Abstract

We clarify the structure of the non-archimedean valuation fieldρ R which was introduced by A. Robinson, and of theρ-non-archimedean hulls of Banach algebras and Lie groups. (For Banach spaces this construction is due to W. A. J. Luxemburg.) In particular, we show that any two infinite-dimensional real normed spaces have a pair of isometrically isomorphicρ-non-archimedean hulls.

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Author notes

  1. Vladimir Pestov

    Present address: Institute of Mathematics, 630090, Novosibirsk, USSR

Authors and Affiliations

  1. Department of Mathematical Analysis, Tomsk State University, 634010, Tomsk, USSR

    Vladimir Pestov

Authors
  1. Vladimir Pestov
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Dedicated to the memory of A. Robinson on the occasion of the 70th anniversary of his birth.

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Pestov, V. On a valuation field invented by A. Robinson and certain structures connected with it. Israel J. Math. 74, 65–79 (1991). https://doi.org/10.1007/BF02777816

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  • DOI: https://doi.org/10.1007/BF02777816

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