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1.
Banach空间中一类扰动优化问题最优解的特征与存在性   总被引:2,自引:0,他引:2  
何金苏 《数学学报》2007,50(3):669-678
设(X,‖·‖)是Banach空间,x∈X,Z是X的非空子集,J是Z→R的下半连续下有界函数.本文研究扰动优化问题min_(z∈Z)(J(z)+‖x-z‖)(记作(J,x)-inf)的最优解的特征和最优解的存在性等问题.我们引入J-太阳集的概念,同时在Z是J-太阳集的情形下,给出了扰动优化问题(J,x)-inf的最优解的“Kolmogorov”型特征刻画.并借助于集合的若干紧性概念和最优值函数的方向导数研究了扰动优化问题(J,x)-inf的最优解的存在性.  相似文献   

2.
设E是Banach空间,T∶E→2E*是极大单调算子,T-10≠ф.令x0∈E,yn=(J λnT)-1xn en,xn 1=J-1(αnJxn (1-αn)Jyn),n0,λn>0,αn∈[0,1],文章研究了{xn}收敛性.  相似文献   

3.
胡长松 《应用数学》2006,19(2):331-335
设E是自反的Banach空间,T∶E→2E是极大单调算子.T-10≠.令x0∈E,yn=(J λnT)-1xn en,xn 1=J-1(αnJxn (1-αn)Jyn),n≥0,λn>0,αn∈[0,1],本文研究了{xn}收敛性.  相似文献   

4.
对于Π_1空间上J-正常算子的J-酉等价问题进行讨论.针对不同情况,给出了Π_1空间上两个J-正常算子J-酉等价的充要条件.这将有助于研究Π_1空间上交换J-von Neumann代数之间的J-酉等价.  相似文献   

5.
Banach空间中线性流形的单值度量投影算子部分   总被引:1,自引:0,他引:1  
为了研究Banach空间集值线性映射包含y∈M(x)的最小范数极值解,其中X,Y为Banach空间,M X×Y为线性流形,本文引入Banach空间X×Y中线性流形的单值度量算子部分,并给出了该算子部分的结构的刻划.为在另文将Lee S J与NashedM Z所引进并研究的Hilbert空间中集值线性映射包含的最小二乘解推广到Banach空间奠定了理论基础.  相似文献   

6.
假设S(X)是Banach空间X的单位球面,作引进了四个新的几何参数:Jε(X)=sup{βε(x),x∈S(X)},jε(X)=inf{βε(x),x∈S(X)},Gε(X)=sup{αε(x),x∈S(X)},gε(X)=inf{αε(x),x∈S(S)},其中≤ε≤1,βε(x)=sup{min{‖x εy‖,‖x-εy‖,y∈S(X)}},αε(x)=inf{max{‖x εy‖,‖x-εy‖,y∈S(X)}},讨论了这些参数的性质,本主要结果是:如果主要结果是:如果有一个ε,0≤ε≤1,使得Jε(X)<1 ε/2或gε(X)>1 ε/3,那末X有一至正规结构。  相似文献   

7.
设X是一致凸空间,G为X中太阳集,R.Smarzewski[1]证明了g∈G对x∈的最佳逼近具有广义强唯一性,本文讨论其逆,在最佳逼近是广义强唯一的条件下,研究了空间的凸性和逼近集的太阳性.  相似文献   

8.
刘立新  张朝晖 《数学学报》2007,50(5):1141-115
设S为至少有一个穿孔点α的Riemann曲面.对于曲线α■S,可以定义关于α■S的Dehn twist t_α.设H是S的映射类群的子群,H中的元素保持α不动,并且投影为S=S∪{α}上平凡的映射类变换.定义t_α是关于α■S的Dehn twist.本文考虑关于X(S上的映射类变换)的方程(t_α■θ)~n■X=圮,其中θ∈H是任意给定的.由于(t_αoθ)~n和t_α~n都投影为关于简单闭曲线■的Dehn twist t_■.所以上述方程在H中的解是存在的.对充分大的n,我们给出上述方程有形如X=θ~(n)的解的充要条件.此外,对任给的θ∈H,刻画了子空间H′■H,这里方程的解X=X_n最终要属于H′.最后,考虑简单映射类变换的某些复合映射,并给出了相应的刻画:它们在沿S上的某些简单曲线做剖分后所得的穿孔pant上是不可约的.  相似文献   

9.
研究Banach空间中积分双半群的生成条件.利用算子A的豫解算子,给出了积分双半群T(t)的生成定理.结果表明:如果对任意的x∈X,f∈X*,以及A|λ]<δ,λ∈ρ(A),有∈Lp(R),则存在算子族S(t),t∈R,S(t)强连续且满足积分双半群的定义.  相似文献   

10.
对于Krein空间上J-正常算子 的各种可定化性进行了研究. 利用可定化J-正常算子的谱函数, 给出了临界线的概念, 得到了可定化的J-正常算子成为强可定化算子和一致可定化算子的充要条件.  相似文献   

11.
θ-连通空间是比连通空间更广泛的一类空间,在前人的研究基础之上得到了局部口一连通空间的充分必要条件,证明了局部θ-连通空间在商映射下是不变的,同时也得到了和空间 α∈AXα与乘积空间Пs∈SX8是局部θ-连通空间的充分必要条件.  相似文献   

12.
Let X be a topological space and let Φ ? C(X). Then there exists a topological space Y containing X as a subspace and such that Φ = C(Y)¦X, if and only if Φ is weakly composition closed, i.e., for any index set I, any fi ∈ Φ (i ∈ I) and any continuous map k : RI → Rwe have k ° 〈fi〉 ∈ Φ, where 〈fi〉 : X → RI is the map with i-th coordinate fi. The analogous statement is valid for functions to any T1 space, rather than to R, and even we can consider functions to any set of T1 spaces, and then a generalization of the above statement is valid, with a suitably defined weak composition closedness property. We also show that some earlier results on characterization of function classes Φ ? C(X) of the form C(Y)¦X, with Y some extension of a given topological space X, and on the characterization of function classes C(〈X, T〉), with T some topology on a given set X, respectively, can be generalized in an analogous way as above, by means of composition properties analogous to the above one or by filter closedness (for functions to any set of T3 spaces, or to any set of topological spaces, respectively).  相似文献   

13.
在一般拓扑空间中给出了强S-仿紧空间的概念,研究了它的性质并给出了Hausdorff空间下它的等价刻画,同时讨论了它的相对性质.  相似文献   

14.
对简单图G=〈V,E〉,如果存在一个映射f:V→{0,1,2,…,2 E-1}满足1)对任意的u,v∈V,若u≠v,则f(u)≠f(v);2)对任意的e1,e2∈E,若e1≠e2,则g(e1)≠g(e2),此处g(e)=f(u)+f(v),e=uv;3){g(e)e∈E}={1,3,5,…,2 E-1},则称G为奇强协调图,f称为G的奇强协调标号.给出了直径为4的树的奇强协调标号.  相似文献   

15.
This paper surveys some of the main convergence properties of the Mann-type iteration for the demicontractive mappings. Some variants of the Mann iteration that ensure the strong convergence, like the (CQ) algorithm and a variant for the asymptotically demicontractive mappings are also considered. The usual framework of our study is a (real) Hilbert space and only to a certain extent some particular Banach spaces. Historical aspects are pointed out and some applications for the convex feasibility problem are discussed.  相似文献   

16.
基于值域的稠密性和闭性,有界线性算子的点谱可进一步细分为互不相交的四个组成部分,即四类点谱.设H_1,H_2,H_3为无穷维复可分Hilbert空间,记M_(D,E,F)=(A D E0 B F0 0 C)∈B(H_1H_2H_3).当对角算子A,B,C固定时,给出了M_(D,E,F)的四类点谱随D,E,F扰动的完全描述.  相似文献   

17.
By using lower bound conditions of the Lévy measure w.r.t. a nice reference measure, the coupling and strong Feller properties are investigated for the Markov semigroup associated with a class of linear SDEs driven by (non-cylindrical) Lévy processes on a Banach space. Unlike in the finite-dimensional case where these properties have also been confirmed for Lévy processes without drift, in the infinite-dimensional setting the appearance of a drift term is essential to ensure the quasi-invariance of the process by shifting the initial data. Gradient estimates and exponential convergence are also investigated. The main results are illustrated by specific models on the Wiener space and separable Hilbert spaces.  相似文献   

18.
It is shown that if E[7] is a locally convex space ordered by a closed, generating positive cone K satisfying certain mild hypotheses relating K and 7, then E′ is lattice-ordered by the dual cone K′ whenever the identity linear transformation on E is the pointwise limit of sums of transformations x→〈x,x′〉z where z∈K and x′∈K′. The converse is true for certain classes of spaces, e.g., Fréchet spaces.  相似文献   

19.
The connection between the approximation property and certain classes of locally convex spaces associated with the ideal ?? of approximable operators will be discussed. It will be shown that a Frechet Montel space has the approximation property iff it is a mixed ??-space, or equivalently, iff its strong dual is a ??-space. Similarly, a Silva space has the approximation property iff it is a mixed ??-space or equivalently iff it is a ??-space. We shall also show that a Frechet Schwartz space with the bounded approximation property is always a ??-space.  相似文献   

20.
On the boson—fermion Fock space F(H, K) associated with two complex Hilbert spaces H and K, there exists a family {Qs | S ∈ C(H, K)} of Dirac type operators, where C(H, K) is the set of densely defined closed linear operators from H to K. A theorem on the strong anticommutativity of two Dirac operators QS and QT is established. As an application, representations on F(H, K) of a supersymmetry algebra arising in a two—dimensional relativistic supersymmetric quantum field theory are discussed.  相似文献   

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