Norms of minimal projections (Q1328327)

The authors prove that the projection constants of two- and three- dimensional spaces are bounded by \({4\over 3}\) and \((1+ \sqrt 5)/2\), 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.