On some non-archimedean normed linear spaces. I
Pierre Robert (1968)
Compositio Mathematica
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Displaying similar documents to “A characterization of the spherically complete normed spaces with a distinguished basis”
On some non-archimedean normed linear spaces. I
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On some non-archimedean normed linear spaces. II
Pierre Robert (1968)
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Kolmogorov diameters and orthogonality in non-Archimedean normed spaces.
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The Kolmogorov n-diameter of a bounded set B in a non-archimedean normed space, as defined by the first author in a previous paper, is studied in terms of the norms of orthogonal subsets of B with n + 1 points.
On the volume method in the study of Auerbach bases of finite-dimensional normed spaces
Anatolij Plichko (1996)
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In this note we show that if the ratio of the minimal volume V of n-dimensional parallelepipeds containing the unit ball of an n-dimensional real normed space X to the maximal volume v of n-dimensional crosspolytopes inscribed in this ball is equal to n!, then the relation of orthogonality in X is symmetric. Hence we deduce the following properties: (i) if V/v=n! and if n>2, then X is an inner product space; (ii) in every finite-dimensional normed space there exist at least two different...