| 1. | A class of lattice - subspace in regular operator space
正则算子空间上的一类格子空间 |
| 2. | The main purpose of the thesis is to study the existence of strongly non - regular operators between classical banach lattices
最后，本文的主要目的是研究经典banach格上强非正则算子的存在性。 |
| 3. | A regularized strategy which is based on the gauss kernel is recommened , and the discrepancy principle to select the regularized parameter is proved
摘要以正则化思想为基础，介绍了基于高斯核来构造正则算子的方法，使其对噪音进行过滤，并证明了类似于正则化方法中选择参数的偏差原理。 |
| 4. | Chapter 4 is mainly about the properties of regular operators . we give two examples to show that regular norm and operator norm may not equal to each other and the module for operator on banach lattice may not exist firstly
第四章研究了一类正则算子的性质，首先行出例子说明正则范数与算子范数一般不相等，而且对任意算子不一定有模存在 |
| 5. | Results firstly the axioms of regular implication are minimized ; furthermore a method of constructing this implication is given ; finally the characterization of some regular implications with specical properies is discussed
结果对正则蕴涵算子的定义进行了简化，进而介绍了一种生成正则蕴涵算子的方法，最后就某些具有特殊性质的正则算子进行了研究，得到了相应的函数特征。 |
| 6. | Then the relation of regular operators , bounded operators and linear operators on banach lattices are given , that is lr ( e , f ) lb ( e , f ) l ( e , f ) ; order dual , operator dual and algebra dual are related , i . e . e " c e * c e #
然后给出banach格空问上正则算子，有界算子和线性算子的关系： lve ； f ） of 。 ef ） clp ， f ） ；给出了序对偶，算子对偶和代数对偶的关系： e ’ ce ” ce个然后引入赋值映射人证明了j是保格运算的格同态 |
| 7. | Then the order bound norm imposed on the order bounded operators between two banach lattices is fully studied . the results include the relationships between the order bound norm and the other two types of norms of a regular operator ; respectively , and a condition under which the space of order bounded operators is a dedekind complete banach lattice
接着讨论了banach格间序有界算子的序有界范数，详细论证了正则算子的(一致)算子范数、正则范数和序有界范数三者之间的关系，并得到了序有界算子空间在序有界范数之下是dedekind完备banach格的一个条件。 |
| 8. | Alternatively , we investigate the relationships between the space of bounded operators and its regular operator subspace with respect to the operator norm topology , thereby answering partially the question of how big the regular operator subspace is and discussing the existence of strongly non - regular operators between some classical banach lattices
这里把这一问题转化为考察有界线性算子空间与它的正则算子子空间在(一致)算子拓扑之下的关系，从而部分的回答了正则算子集合在有界线性算子空间中有多大的问题，解决了经典banach格上强非正则算子的存在性。 |
