Norms of Minimal Projections
Hermann König, Nicole Tomczak-Jaegermann
Abstract
It is proved that the projection constants of two- and three-dimensional spaces are bounded by 4/3 and (1+ 5)/2, respectively. These bounds are attained precisely by the spaces whose unit balls are the regular hexagon and dodecahedron. In fact, a general inequality for the projection constant of a real or complex n-dimensional space is obtained and the question of equality therein is discussed.
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