Normal property, Jamenson property, CHIP and linear regularity for an infinite system of convex sets in Banach spaces

摘要

In this paper, we study different kinds of normal properties for infinitesystem of arbitrarily many convex sets in a Banach space and provide the dualcharacterization for the normal property in terms of the extended Jamensonproperty for arbitrarily many weak*-closed convex cones in the dual space.Then, we use the normal property and the extended Jamenson property to studyCHIP, strong CHIP and linear regularity for the infinite case of arbitrarilymany convex sets and establish equivalent relationship among these properties.In particular, we extend main results in [3] on normal property, Jamensonproperty, CHIP and linear regularity for finite system of convex sets in aHilbert space to the infinite case of arbitrarily many convex sets in Banachspace setting.