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半范     
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  semi-norm
     A Necessary and Sufficient Condition for the Normal Family of Vector-valued Analytic Functions in the Semi-Norm Space
     取值于半范线性空间中的全纯函数族的正规性
短句来源
     We establish two types of inverse theorems which correspond respectively to ordinary standard-Bernstein method and Lorentz-Berens method Because of having no conception of derivative in abstract space c(X), we deal with semi-norm and interpolation space by means of generalized Lip-semi-norm and generalized Lip-classes.
     依据不同条件,我们建立了两种类型的逆定理,它们分别相应于通常正算子逼近理论中的标准Bernstein方法和Lorentz—Berens方法. 由于抽象空间C(X)没有定义导数概念,我们在处理半范与插补空间时是借助于广义Lip半范和广义Lip类来实现的.
短句来源
     The relation between fuzzy pseudo semi-norm and balanced, Q-absorbing and semi-convex fuzzy set is investigated. A characterization of locally semi-convex fuzzy topological vector space in terms of a family of fuzzy pseudo semi-norms is proved.
     研究了Fuzzy拟半范与均衡、Q-吸收、半凸Fuzzy集之间的关系,证明了局部半凸Fuzzy拓扑线性空间可借助于一族Fuzzy拟半范来表征.
短句来源
  semi-normed
     A Version of Ekeland's Variational Principle in Countable Semi-Normed Spaces
     可数半范空间中Ekeland变分原理的一种形式(英文)
短句来源
     In this paper, we define two sequence spaces l_∞( M , p ,q)、l_1(M,p,q) on semi-normed complex linear space X=( p ,q)(where is seminorm), by using Orlicz function and we give various properties and some inclusion relations on these spaces. Chapter 1 introduction presents the significance and development of Orlicz sequence space.
     本文主要在半范空间X = ( X , q)上通过Orlicz函数作了两个序列空间、,并讨论了一些性质及集合的包含关系. 本文分为4章,主要内容有: l_∞( M , p ,q)(l1 M , p ,q)在第1章绪论中主要论述了Orlicz序列空间研究的目的意义及现状。
短句来源
     In this paper, we obtain general form for hounded law of the iterated logarithm for a sequence of independent random vectors taking values in a semi-normed measurable vector space from which some results:of J.
     本文给出了取值于半范可测向量空间上独立随机元序列的有界重对数律的一般形式,由此进一步推广了Kuelbs J.
短句来源
     The present paper represents moment inequalities for sums of independent random vectors taking values in a semi-normed measurable vector space about function of a certain type specially designated, and de Acosta's theorem is the special case of this result.
     本文得到了取值于半范可测向量空间上的独立随机元之和关于某一类特定函数的矩不等式。 de Acosta等人的定理均为该结果的特例。
短句来源
     In this paper, a now version of Ekeland's variational principle in countable semi-normed spaces is given.
     本文给出了可数半范空间中Ekeland变分原理的一种新的形式.
短句来源
  semi-norms
     The relation between fuzzy pseudo semi-norm and balanced, Q-absorbing and semi-convex fuzzy set is investigated. A characterization of locally semi-convex fuzzy topological vector space in terms of a family of fuzzy pseudo semi-norms is proved.
     研究了Fuzzy拟半范与均衡、Q-吸收、半凸Fuzzy集之间的关系,证明了局部半凸Fuzzy拓扑线性空间可借助于一族Fuzzy拟半范来表征.
短句来源
  seminormed
     A Characterization for A Family of Canonical Module Homomorphisms on Random Seminormed Modules to be Equicontinuous
     随机半范模上等度连续的典则模同态族的特征
短句来源
     Study on some properties of fuzzy seminormed spaces
     模糊赋半范空间的性质研究(Ⅰ)
短句来源
     Study on some properties of fuzzy seminormed spaces(Ⅱ)
     模糊赋半范空间的性质研究(Ⅱ)
短句来源
     At present paper,norms in C(R) and L~P[R] linear space were defined. (C(R)),‖·‖(·)) and L~P[R],‖·‖(·)) were fuzzy seminormed spaces through proving. Some properties of the fuzzy seminormed spaces were studied.
     定义了线性空间C(R)和LP[R]上的模糊范数,证明了(C(R)),‖·‖(·))和(LP[R],‖·‖(·))是模糊赋半范空间,并对它们的性质进行了研究。
短句来源
     In this paper,the two completeness of fuzzy seminormed spaces,ie. the completeness about its crisp topological structure(τ-completeness),and the completeness about its fuzzy topological structure(-τ-completeness),are investigated.
     研究了模糊赋半范空间的两种完备性,即关于分明拓扑结构的完备性(τ-完备)和模糊拓扑结构的完备性( τ—完备)。
短句来源

 

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  semi-norm
We prove that given a real JB*-triple E, and a real Hilbert space H, then the set of those bounded linear operators T from E to H, such that there exists a norm one functional and corresponding pre-Hilbertian semi-norm on E such that
      
We establishO(h) estimates of the error in a discreteH1 semi-norm.
      
The measure of the generalized input function,Λ, which is a multiplet inF, the deformation gradient;θ, the temperature;g = gradθ, as well as various chemical affinities,Ak; is given by a semi-norm over aBanach space.
      
For a generator $A$ of a $C_0$-semigroup $T(\cdot)$ on a Banach space $X$ we consider the semi-norm $M^{k}_x:=\limsup_{t\to 0+}\|t^{-1}(T(t)-I)A^{k-1}x\|$ on the Favard space ${\cal F}_{k}$ of order $k$ associated with $A$.
      
The use of this semi-norm is motivated by the functional analytic treatment of time-discretization methods of linear evolution equations.
      
更多          
  semi-normed
A Characterization of Continuous Module Homomorphisms on Random Semi-Normed Modules and Its Applications
      
LetXn, n∈?d be a field of independent random variables taking values in a semi-normed measurable vector spaceF.
      
This time series problem is presented in the general framework of regression estimation from dependent samples with regressor valued in some infinite dimensional semi-normed vectorial space.
      
Semi-normed vector spaces with duals of integral type
      
We introduce the notion of a temperate map, with respect to a given asymptotic scale, between two locally convex metrisable semi-normed spaces.
      
  semi-norms
The principal coefficients of the operator are assumed to be in BMO space with their BMO semi-norms small enough.
      
On the continuity of semi-norms on operator algebras
      
On the Hilbert-Schmidt semi-norms ofL1 of a nilpotent Lie group
      
It is assumed that the boundary of a bounded domain is well approximated by hyperplanes at every point and at every scale, and that the tensor coefficients belong to BMO space with their BMO semi-norms sufficiently small.
      
Error estimates in W2,∞-semi-norms for discrete interpolating D2-splines
      
更多          
  seminormed
Optimal approximation and error bounds in seminormed spaces
      
The optimization theory in seminormed spaces and a practical method of solution are developed by resorting to duality theorems and more specially to the theory of convex bodies.
      
We obtain a geometrical description of the class of all homeomorphisms ?:G→ G' that induce bounded operators ?* from the seminormed Sobolev spaceLp1(G') toLp1(G) by the rule ?*u =u o ?.
      
On the barrelledness oflp-direct sums of seminormed spaces for 1≦p≦∞
      
Direct and converse imbedding theorems for seminormed spaces
      
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  其他


In this paper we discuss inverse theorems of Gonska's theorems [1] on the approximation by positive linear operators from C(X) into B(Y). We establish two types of inverse theorems which correspond respectively to ordinary standard-Bernstein method and Lorentz-Berens method Because of having no conception of derivative in abstract space c(X), we deal with semi-norm and interpolation space by means of generalized Lip-semi-norm and generalized Lip-classes.

Gonska建立了由抽象空间C(X)到B(Y)的正线性算子逼近的量化定理[1],本文讨论它的逆定理.依据不同条件,我们建立了两种类型的逆定理,它们分别相应于通常正算子逼近理论中的标准Bernstein方法和Lorentz—Berens方法.由于抽象空间C(X)没有定义导数概念,我们在处理半范与插补空间时是借助于广义Lip半范和广义Lip类来实现的.最后,将所得的结果应用于二元正算子逼近.得到二元Vallee—Pousson算子的一个逼近逆定理.

In references (Ⅰ) , a necessary and sufficient condition for the normal fa-mily of vector-valued analytic functions is obtained in Banach spaces. In thispaper, we have proved that the conclusion is still right in semi-norm linearspaces.

全纯函数正规族的理论在复变函数中起着重要作用。定义域在复数域而取值于半范线性空间上的抽象函数叫做向量值函数。本文运用线性拓扑空间的结论与方法,讨论了向量值全纯函数正规族的一个充分条件,从而推广了文献[1]中的结论。

In this paper We introduced the concept of the single-valued extension, property and u-Spectral functions on a locally convex space, and extend Some main results in the references [1]

本文引入了局部凸空间中连续线性算子的单值扩张性和u—谱函数的概念,把文献[1]的单值扩张性和u—谱函数等的一些主要性质推广到局部凸空间。 线性算子理论从有限维空间利用矩阵方法研究发展到Hilbert空间上的自伴算子,正规算子及Banach空间上的谱算子,可分解算子和μ—谱函数,其研究方法较有限维情形有了很大的突破。迄今为止,已形成了十分丰富的算子理论。从六十年代初可分解算子和u—谱函数概念的引进之后,人们对它进行了各种的推广,例如,把它推广到无界闭算子的情形而引进了无界广义标算子的概念,然而都是限于对Banach空间上算子的研究。众所周知,实际问题中出现的空间不仅有Banach空间,而且还有大量的是局部凸空间。例如,广义函数所讨论的空间C_c~∞(Ω)就是局部凸的完备空间(本文空间均指Hausdorff空间),常见的 C~k(Ω)(o≤k≤∞)亦是局部凸空间。因此人们不仅要研究Banach空间中算子的谱理论,而且有必要研究局部凸空间中算子的谱理论。由于Banach空间的拓扑仪由一个半范决定,而局部凸空间却是由一族半范决定的。因此在局部凸空间上研究问题时需要考虑的因素比Banach空间更...

本文引入了局部凸空间中连续线性算子的单值扩张性和u—谱函数的概念,把文献[1]的单值扩张性和u—谱函数等的一些主要性质推广到局部凸空间。 线性算子理论从有限维空间利用矩阵方法研究发展到Hilbert空间上的自伴算子,正规算子及Banach空间上的谱算子,可分解算子和μ—谱函数,其研究方法较有限维情形有了很大的突破。迄今为止,已形成了十分丰富的算子理论。从六十年代初可分解算子和u—谱函数概念的引进之后,人们对它进行了各种的推广,例如,把它推广到无界闭算子的情形而引进了无界广义标算子的概念,然而都是限于对Banach空间上算子的研究。众所周知,实际问题中出现的空间不仅有Banach空间,而且还有大量的是局部凸空间。例如,广义函数所讨论的空间C_c~∞(Ω)就是局部凸的完备空间(本文空间均指Hausdorff空间),常见的 C~k(Ω)(o≤k≤∞)亦是局部凸空间。因此人们不仅要研究Banach空间中算子的谱理论,而且有必要研究局部凸空间中算子的谱理论。由于Banach空间的拓扑仪由一个半范决定,而局部凸空间却是由一族半范决定的。因此在局部凸空间上研究问题时需要考虑的因素比Banach空间更多。文献[1]对算子的单值扩张性和u—谱函数进行了较系统的研究,但它是对Banach空间进行的。[8]在局部凸空间中研究了u—谱函

 
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