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/