Large subspaces ofl∞n and estimates of the gordon-lewis constantand estimates of the gordon-lewis constant

Lower bounds are obtained for the gl constants and hence also for the unconditional basis constants of subspaces of finite dimensional Banach spaces. Sharp results are obtained for subspaces of l(Formula presented.), while in the general case the gl constants of “random large” subspaces are related to the distance of “random large” subspaces to Euclidean spaces. In addition, a new isometric characterization of l(Formula presented.) is given, some new information is obtained concerning p-absolutely summing operators, and it is proved that every Banach space of dimension n contains a subspace whose projection constant is of order n1/2. © 1980, The Weizmann Science Press of Israel. All rights reserved.

Large subspaces ofl∞n and estimates of the gordon-lewis constantand estimates of the gordon-lewis constant Academic Article