1) continuous linear functional
连续线性泛函
1.
We give a sufficient & necessary condition for the Existence of non-trivial continuous linear functional on top-ological vector spaces, and show that there is no non-trivial continuous linear functional on any quasi-bounded topological vector space.
给出了拓扑线性空间上存在非零连续线性泛函的一个充要条件,并由此证明了在任意拟有界的拓扑线性空间上均不存在非零连续线性泛函。
2.
Under the necessary condition of an extremum of a continuous linear functional the least upper bound of Fourier coefficients of univalent harmonic mappings is obtained.
利用连续线性泛函取得极值的必要条件,得到关于单叶调和映射的傅立叶系数的上确界,推广了PeterDuren的研究方法。
3.
The necessary and sufficient condition for existing no non-zero continuous linear functional in spaces L￣p(Ω,μ)(0<p<1)is there existing no atomic set in(Ω,μ).
空间Ｌ（Ω，μ）（０＜ｐ＜１）上不存在非零连续线性泛函的充要条件是（Ω，μ）中不存在原子集合，２。
2) continuous linear functionals
连续线性泛函
1.
The reflexity and the approximation property in Banach space X are studied by use of T semi inner product (x,y) T= lim t→0 +[(‖x+ty‖ 2-‖x‖ 2)/(2t)],x,y∈X and a class of continuous linear functionals T(X)={f x∈X *|〈f x,y〉=(x,y) T ;x,y∈X} is defined.
利用Ｔａｐｉａ半内积（ｘ，ｙ）Ｔ＝ｌｉｍｔ→０＋［（ｘ＋ｔｙ２－ｘ２）／（２ｔ）］，ｘ，ｙ∈Ｘ，研究了Ｂａｎａｃｈ空间Ｘ的自反和逼近性质，并在光滑的Ｂａｎａｃｈ空间Ｘ上利用由Ｔａｐｉａ半内积定义的一类连续线性泛函Ｔ（Ｘ）＝｛ｆｘ∈Ｘ＊｜〈ｆｘ，ｙ〉＝（ｘ，ｙ）Ｔ；ｘ，ｙ∈Ｘ｝研究了Ｂａｎａｃｈ空间的严格凸、一致凸以及具有性质（Ｈ）的特征。
2.
This paper shows that, on a complete random normed module, there exists a nonzero continuous linear functional if and only if there is at least one atom in its base space; and there exist suffciently many nonzero continuous linear functionals if and only if its base is essentially generated by at most an countable family of atoms.
本文证明了在任意满支承的随机赋范模上存在一个非零连续线性泛函的充要条件是它的基底空间至少存在一个原子;存在足够多非零连续线性泛函的充要条件是它的基底空间本质上由至多可数个原子生成。
3.
This paper shows that on a complete random normed module,there exists a nonzero continuous linear functional if and only if there is at least an atom in its base space;and there exist sufficiently many nonzero continuous linear functionals if and only if its base is essentially generated by an at most countable family of atoms.
本文证明了在完备的随机赋范模上，存在一个非零连续线性泛函的充要条件是它的基底空间至少存在一个原子；存在足够多非零连续线性泛函的充要条件是它的基底空间本质上由至多可数个原子生成。
3) bilinear continuous functional
双线性连续泛函
4) weak continuity of nonlinear functions
非线性泛函的弱连续性
5) random Hahn-Banach theorem
随机线性连续泛函
6) The Kernel of a Continuous Linear Functional
连续线性泛函的核
补充资料：连续函子
连续函子
continuous functor
连续函子【。川如以.加叱加r;.曰甲印“~曲巾y毗oP] “与极限可交换的函子”的概念的同义词.设叽与母为有极限的范畴.一个l位共变函子只讯~落称为连续的(coniin因璐)，如果对于任何图J:勿~服都有F(1而J)=1而JF.这里的勿是一个任意的小图概形.更具体地，上述等式的意义如下:如果(A;料。，D已勿)是图J的极限，而拜。:A~J(D)(DCOb勿)是出现在极限定义中的态射，那么(F(A);F伽。)，D任Ob勿)是图JF:勿~C的极限. 一个函子F:服一伍是连续的，当且仅当它与任意一族对象之积可交换，也可与任何态射对的核可交换.从况到集合的范畴的每个基本函子凡(X)二马(A，X)都是连续的.M.m.U~KO撰(补注1
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参考词条