CAJ | 학술논문

设N是一个赋范线性空间X上的套,m(N)是N到N的映射全体所成的集合,记m0(N)={α∈m(N)|α(0)=0,α左连续且保序}.对于子空间M,首先表明下面命题是等价的:(1)M是弱闭的AlgN-模;(2)存在α∈m_0(N)使M=M_α;(3)存在β∈m(N)使M=M_β.假使N最多只包含3个元素,那么所有的AlgN-模可全部被列举出来;假如N至少包含4个元素,那么下面命题是等价的:(1)0<0~+且X-<X;(2)AlgN中存在极小的弱闭理想;(3)存在极大的弱闭外AlgN-模.进一步,假设N是非平凡套,那么,N中存在间断点当且仅当AlgN中存在极大的弱闭理想.假设N至少含4个元素,那么,N中存在2-阶间断点当且仅当存在极小弱闭外AlgN模.上述结果也可用紧套代数中的范数闭模来刻画.
설N시일개부범선성공간X상적투,m(N)시N도N적영사전체소성적집합,기m0(N)={α∈m(N)|α(0)=0,α좌련속차보서}.대우자공간M,수선표명하면명제시등개적:(1)M시약폐적AlgN-모;(2)존재α∈m_0(N)사M=M_α;(3)존재β∈m(N)사M=M_β.가사N최다지포함3개원소,나요소유적AlgN-모가전부피열거출래;가여N지소포함4개원소,나요하면명제시등개적:(1)0<0~+차X-<X;(2)AlgN중존재겁소적약폐이상;(3)존재겁대적약폐외AlgN-모.진일보,가설N시비평범투,나요,N중존재간단점당차부당AlgN중존재겁대적약폐이상.가설N지소함4개원소,나요,N중존재2-계간단점당차부당존재겁소약폐외AlgN모.상술결과야가용긴투대수중적범수폐모래각화.
Let N be a nest on a fixed linear norm space X, m(N) be the set of all maps of N into itself, put m_0(N)={α∈m(N)α(0)=0, α is order preserving and left continuous}. For a subspace M, we first show that the following three statements are equivalent: (1)M is a weakly closed AlgN-module; (2)there exists α∈m_0(N) such that M=M_α; (3)there exists β∈m(N) such that M=M_β. If N contains 3 elements at most, the all weakly closed AlgN-modules can be listed; if N contains 4 elements at least, then the following statements are equivalent: (1)0<0~+and X~-<X; ( 2 ) there exists minimal weakly closed idea of AlgN; (3) there exists maximal outer weakly closed AlgN-module.Moreover, suppose Nbe a non-trivial nest, then there exists discontinuous point in N if and only if there exists maximal weakly closed ideal of AlgN. Suppose N contain 4 elements at least, then there exists a two-order discontinuous point in N if and only if there exists minimal outer weaklv closed ,AlgN-module.