A characterization and equations for minimal shape-preserving projections

Let X denote a (real) Banach space and V an n-dimensional subspace. We denote by B = B(X, V) the space of all bounded linear operators from X into V; let P(X, V) be the set of all projections in M. For a given cone S subset of X, we denote by P = P-S (X, V) the set of operators P is an element of P such that P S subset of S. When P-S not equal 0, we characterize those P is an element of P-s for which parallel to P parallel to is minimal. This characterization is then utilized in several applications and examples. (C) 2005 Elsevier Inc. All rights reserved.