摘要
对偶不变性结果是泛函分析空间理论的核心内容.随着分析学中测度理论等研究的深入,各领域相继出现了不变性定理,如Orlicz-Pettis定理,Schur引理等.因此,扩大已知对偶不变性的不变范围,乃至求得最大不变范围显然有重要意义.找到了函数级数的向量序列赋值收敛具有全程不变性的充要条件是(E,β(E,Eβ))是AK-空间,并且证明了文[1]中的主要定理是本结果的一个推论.
Duality invariance is the core of the space theory of functional analysis. With the developments of measure theory and so on, the invariance theorems appear in many fields. For example, the Orlicz - Pettis theorem and the Schur lemma. So expanding the invariant ranges of duality invariance and even finding the maximum invariant ranges are evidently important. It is shown that the sufficient and necessary condition for the sequential evaluation convergence of vectors of function series to be having the full invariance is that （ E,β（ E,E^β） ） is an AK - space. It is also proved that the result in [ 1 ] is a corollary of this this theorem.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2006年第2期192-194,共3页
Journal of Natural Science of Heilongjiang University
