关于偶泛函临界点理论中的空间可分性假设

On the Separability of Space in the Critical Point Theory for Even Functionals

凭借本文中证明的一个引理,在关于偶泛函临界点的某些定理中,可以去掉空间可分性的假设.

The following lemma is proved:Let X be a reflexive Banach space,f:X→R continuous with respect to the weak topology on X,f(θ)=0.Then,for any given ε>0,there exists a finite-dimensional linear subspace X_mof X and a linear projection operator Pm:X→Xm and a positive constantδ such that‖P_mx‖≥δfor all x∈X\f^(-1){(-ε,ε)}.Using this lemma,theauthor takes off the separability of space in some theorems in the criticalpoint theory for even functionals.