Applications of spherical designs to Banach space theory

Volume 64 / 2004

Hermann König Banach Center Publications 64 (2004), 127-134 MSC: Primary 46B20. DOI: 10.4064/bc64-0-10

Abstract

Spherical designs constitute sets of points distributed on spheres in a regular way. They can be used to construct finite-dimensional normed spaces which are extreme in some sense: having large projection constants, big or small Banach-Mazur distance to Hilbert spaces or $\ell_p$-spaces. These examples provide concrete illustrations of results obtained by more powerful probabilistic techniques which, however, do not exhibit explicit examples. We give a survey of such constructions where the geometric invariants can be estimated quite precisely.

Authors

  • Hermann KönigMathematisches Seminar,
    Universität Kiel,
    24 098 Kiel,
    Germany
    e-mail

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