半范数p_A的特征  

Characterization of Semi-Norm p_(A)

作　　者：施慧华[1] SHI Huihua(School of Mathematics Science,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2021年第6期844-848,共5页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金资助项目(11401227,11226129)。

摘　　要：记A={a_(i)}_(i=1)^(∞)={(a_(i,j))(j=1)^(∞)}(i=1)^(∞)■S_(l1)^(+),其中,S_(l1)^(+)={x=(x(n))∈l_(1):‖x‖=1,x(n)≥0,■n∈N},p_(A)(x)=lim_(i→∞)sup∑_(j=1)a_(i,j)|x(j)|,则lim_(i→∞)Si≡lim_(i→∞)sup_(j)a_(i,j)=0,当且仅当对任意非空集合B■N,任意0≤β≤p_(A)(χB),均存在C■B,满足p_(A)(χC)=β.对B■N,记φ_(A)(B)=p_(A)(χB),证明了φ_(A)的强无原子性当且仅当理想I_(A)={A■N:p_(A)(χA)=0}的无原子性.Let A={a_(i)}_(i=1)^(∞)={(a_(i,j))(j=1)^(∞)}(i=1)^(∞)■S_(l1)^(+),where S_(l1)^(+)={x=(x(n))∈l_(1):‖x‖=1,x(n)≥0,■n∈N},p_(A)(x)=lim_(i→∞)sup∑_(j=1)a_(i,j)|x(j)|,则lim_(i→∞)Si≡lim_(i→∞)sup_(j)a_(i,j)=0,if and only if for any nonempty subset B■N,any 0≤β≤p_(A)(χB),there always exists C■B such that p_(A)(χC)=β.LetφA(B)=p_(A)(χB)for B N,it is also proved thatφ_(A)is strong nonatomic if and only if ideal I_(A)={A■N:p_(A)(χA)=0}is nonatomic.

关 键 词：半范数p_(A) A-收敛 强无原子次测度 无原子理想 

分 类 号：O177.2[理学—数学]