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 -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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-10,
author = {Hermann K\"onig},
title = {Applications of spherical designs to Banach space theory},
journal = {Banach Center Publications},
volume = {65},
year = {2004},
pages = {127-134},
zbl = {1061.46009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-10}
}
Hermann König. Applications of spherical designs to Banach space theory. Banach Center Publications, Tome 65 (2004) pp. 127-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-10/