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Compact convex sets and complex convexity

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Abstract

We construct a quasi-Banach space which cannot be given an equivalent plurisubharmonic quasi-norm, but such that it has a quotient by a one-dimensional space which is a Banach space. We then use this example to construct a compact convex set in a quasi-Banach space which cannot be affinely embedded into the spaceL 0 of all measurable functions.

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Author notes

  1. N. J. Kalton

    Present address: Department of Mathematics, University of Missouri, 65211, Columbia, MO, USA

Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, 29208, Columbia, SC, USA

    N. J. Kalton

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  1. N. J. Kalton
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Kalton, N.J. Compact convex sets and complex convexity. Israel J. Math. 59, 29–40 (1987). https://doi.org/10.1007/BF02779665

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  • DOI: https://doi.org/10.1007/BF02779665

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