关于对偶映射的几个结果

本文证明了几个关于对偶映射的命题。说明了实Banach空间X是一致凸的或严格凸的,可等价于X的对偶映射满足一定条件。证明了自反实Banach空间的对偶映射与X的极大单调算子之和的值域为X~*

Some Results on the Duality Mapping

This paper gives some new results on the duality mapping. Let F be the duality mapping of a Banach space X. The main propositions in the paper are Proposition 1. 1. A real Banach space X is strictly convex if and only if F ( X )∩ F ( y ) =Φ whenever x, y ∈X, x≠y. Proposition 1. 3. A real Banach space X is uniformly convex ifand only if that X is reflexive and for every eeeeeeeeeeeeee> 0, there is a number δ< 0 suchthat, for all x, y in X,the conditions ||x||≤1, ||y||≤1 and||x-y||≥ε imply |F(x)-F(y) l>δ Proposition 2. 1. Let X be a real reflexive Banach space, then R ( A + F)=* for every maximal mono'tone operator A and every real number λ> 0 ,