Projectors on Convex Sets in Reflexive Banach Spaces.

摘要

The projector on a convex set K in a reflexive Banach space X is the mapping P(K) assigning to each point x* in the dual space X* the set of points minimizing 1/2 absolute value (x* squared) + 1/2 absolute value (x squared) - over K. Projectors are discussed and shown to enjoy most of the properties of nearest point mappings in Hilbert space. (Author)