摘要
在Banach格及其上的算子理论中,正则算子是一类非常有趣的算子,它扮演着重要的角色.目前,国内外有很多关于算子的正则性的研究成果,但是没有准确的方法来说明连续线性算子的正则性.从而,很自然地会考虑到条件比它要弱的算子,这就是Banach格上的广义正则算子.首先从理论上证明了非广义正则紧算子的存在性;然后分别对定义域和值域空间是离散的和连续的两种情形,具体构造出了非广义正则紧算子的反例.这两个反例同时也说明了M-和L-弱紧算子不是广义正则的.
The regular operators on Banach lattices play very important and interesting role in the literature of Banach lattice and operator theory.There are number of results concerning the regularity of operators,but there is no exact way in the literature to conclude the regularity of continuous linear operators.It is natural and interesting to consider a weaker property,so-called Preregularity of operators on Banach lattices.We first show the existence of non-preregular compact operators on Banach lattices.Then,we present the counterexamples respectively for discrete and continuous domains and range spaces.These examples also show that weakly compact may not be preregular.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2012年第6期788-790,共3页
Journal of Sichuan Normal University（Natural Science）
基金
四川省应用基础研究基金(2010JY0067)资助项目
