首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 125 毫秒
1.
Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k ≥ 2 be an integer and φ a weakly continuous linear surjective map from B(X) into itself. It is shown that φ is k-potent preserving if and only if it is k-th-power preserving, and in turn, if and only if it is either an automorphism or an antiautomorphism on B(X) multiplied by a complex number λ satisfying λk-1= 1. Let A be a von Neumann algebra and B be a Banach algebra, it is also shown that a bounded surjective linear map from A onto B is k-potent preserving if and only if it is a Jordan homomorphism multiplied by an invertible element with (k - l)-th power I.  相似文献   

2.
Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B(X). A map Φ :A →A is said to be strong 3-commutativity preserving if [Φ(A), Φ(B)]3 = [A,B]3 for all A,B∈ A, where[A,B]3 is the 3-commutator of A,B defined by[A, B]3 = [[[A, B],B],B] with [A,B] = AB-BA. The main result in this paper is shown that.,if Φ is a surjective map on A, then Φ is strong 3-commutativity preserving if and only if there exist a functional h : A →F and a scalar λ∈ F with λ~4 = 1 such that Φ(A)=λ A+h(A)I for all A ∈ A.  相似文献   

3.
Let X be a smooth projective curve of genus g 2 over an algebraically closed field k of characteristic p0,and F:X→X(1)the relative Frobenius morphism.Let M s X(r,d)(resp.M ss X(r,d))be the moduli space of(resp.semi-)stable vector bundles of rank r and degree d on X.We show that the set-theoretic map S ss Frob:M ss X(r,d)→M ss X(1)(rp,d+r(p-1)(g-1))induced by[E]→[F(E)]is a proper morphism.Moreover,the induced morphism S s Frob:M s X(r,d)→M s X(1)(rp,d+r(p-1)(g-1))is a closed immersion.As an application,we obtain that the locus of moduli space M s X(1)(p,d)consisting of stable vector bundles whose Frobenius pull backs have maximal Harder-Narasimhan polygons is isomorphic to the Jacobian variety Jac X of X.  相似文献   

4.
The author proves several embedding theorems for finite covering maps,principal G-bundies into bundles.The main results are 1. Let π:E→X be a finite covering map, and X a connected locally path-connected paracompact space. If cat X≤k, then the finite covering space π:E→X can be embedded into the trivial real k-plane bundle. 2. Let π:E→X be a principal G-bundle over a paracompact space. If there exists a linera action of Gon F(F=R or C)and cat X≤k ,then π:E→X can be embedded into ξ1 … ξn for any F-vector bundles ξi,i=1,…k.  相似文献   

5.
Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 : K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence {k(i)n}  [1, ∞)(i = 1, 2), and F := F(T1)∩F(T2) = . An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If E has also a Fr′echet differentiable norm or its dual E*has Kadec-Klee property, then weak convergence theorems are obtained.  相似文献   

6.
Let (X, X) be a pair of real reflexive Banach spaces,and X be X's dual space.We assume without loss of generality that X and X are strictly convex(See Asplund [1]).Let A and B be two maximal monotone mappings from X into 2~x.Attoueh [2] has shown that when X=X is a real Hilbert space,if Int(D(A)-  相似文献   

7.
FIXED POINT THEOREMS FOR MULTI-VALUED MAPPINGS IN LOCALLY CONVEX SPACES   总被引:1,自引:0,他引:1  
江嘉禾 《数学学报》1982,25(3):365-373
<正> Throughout the present paper it is assumed that E is a real,locally convex,Hausdorfftopological vector space,and X(?)E a nonempty compact convex subset.A multi-valuedmapping F:X→2~E is said to be upper(lower) semicontinuous if for any open(closed) setU(?)E the set{x∈X|F(x)(?)U)is open (closed) in X;or,equivalently,for any closed(open) set V(?)E the set{X∈X|F(x)∩ V(?)(?)}is closed (open) in X.Moreover,F  相似文献   

8.
§1. Introduction Let ((Ω, F, P) be a probability space, E be a separable Banach space with norm ‖·‖, and let (X_n, F_n)_(n≥1) be an E-valued adapted sequence, i.e., (F_n)_(n≥1) is a family of increasing sub-σ-algebras of F and X_n is a strongly F_n-measurable E-valued random variable (n≥1). A stopping time (with respect to (F_n)_(n≥1) is a mapping t: Ω→ {1, 2,…} U  相似文献   

9.
Let XH = {XH(s),s ∈RN1} and X K = {XK(t),t ∈R N2} be two independent anisotropic Gaussian random fields with values in R d with indices H =(H1,...,HN1) ∈(0,1)N1,K =(K1,...,KN2) ∈(0,1) N2,respectively.Existence of intersections of the sample paths of X H and X K is studied.More generally,let E1■RN1,E2■RN2 and FRd be Borel sets.A necessary condition and a sufficient condition for P{(XH(E1)∩XK(E2))∩F≠Ф}>0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1×E2×F in the metric space(RN1+N2+d,) are proved,where  is a metric defined in terms of H and K.These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.  相似文献   

10.
Let X(1)= {X(1)(s), s ∈ R+ } and X(2)= {X(2)(t), t ∈ R+ } be two independent nondegenerate diusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X(1)and X(2)are studied. More generally, let E1, E2 ■(0, ∞) and F  Rd be Borel sets. A necessary condition and a suffcient condition for P{X(1)(E1) ∩ X(2)(E2) ∩ F = φ} 0 are proved in terms of the Bessel-Riesz type capacity and Hausdor measure of E1 ×E2 ×F in the metric space(R+ ×R+ ×Rd, ρ), where ρ is an unsymmetric metric defined in R+ × R+ × Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.  相似文献   

11.
Concepts of g-supersolution ,g-martingale,g-supermartingale are introduced,wihch are related to BSDE with Brownian motion and Poisson Point process.A strict comparison theorem,monotonic limit theorem related to this type of BSDE are also discussed.As an application of these results,a nonlinear Doob-Meyer decomposition theorem is obtained.  相似文献   

12.
1IntroductionAs we well know,the study of the local existence of discontinuous solutions to semilinearor quasi-linear hyperbolic systems in higher dimension spaces has attracted considerable at-tention of many well-known mathematicians,thanks to A.Majda’…  相似文献   

13.
The author studies the optimal investment stopping problem in both continuous and discrete cases, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth.Based on the work of Hu et al. (2018) with an additional stochastic payoff function,the author characterizes the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equations (BSDEs for short) with unbounded terminal condition. In regard to the discrete problem, she gets the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provides some useful a priori estimates about the solutions with the help of an auxiliary forward-backward SDE system and Malliavin calculus. Finally, she obtains the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.  相似文献   

14.
基于倒向随机微分方程(BSDE)和非线性期望理论中惩罚方法的启发,研究并得到了一般时间区间上L~p-半狹序列的单调极限定理.该结果的证明并非经典结果的平凡推广,新的框架让我们面对许多新问题,它将在一般框架下g-上鞅的Doob-Meyer型分解以及受限BSDE解的存在性等问题的探索中发挥重要作用.  相似文献   

15.
本文讨论空间形式中子流形的象半径及体积增长的估计。作为应用,用γ-平均曲率的语言获得了一个紧致超曲面的不存在性定理,它是经典紧致极小超曲面不存在性定理的推广.  相似文献   

16.
Spatial scan density (SSD) estimation via mixture models is an important problem in the field of spatial statistical analysis and has wide applications in image analysis. The “borrowed strength” density estimation (BSDE) method via mixture models enables one to estimate the local probability density function in a random field wherein potential similarities between the density functions for the subregions are exploited. This article proposes an efficient methods for SSD estimation by integrating the borrowed strength technique into the alternative EM framework which combines the statistical basis of the BSDE approach with the stability and improved convergence rate of the alternative EM methods. In addition, we propose adaptive SSD estimation methods that extend the aforementioned approach by eliminating the need to find the posterior probability of membership of the component densities afresh in each subregion. Simulation results and an application to the detection and identification of man-made regions of interest in an unmanned aerial vehicle imagery experiment show that the adaptive methods significantly outperform the BSDE method. Other applications include automatic target recognition, mammographic image analysis, and minefield detection.  相似文献   

17.
Using a fixed point theorem,this paper discusses the existence and uniqueness of positive solutions to a system of nonlinear delay fractional differential equations and obtains some new results.  相似文献   

18.
吴盼玉 《数学进展》2012,(3):276-284
本文给出了当终端时间趋于无穷时一类有限时间区间上的倒向随机微分方程的解的收敛性,并且证明了这类解平方收敛到特定的无穷时间区间上的倒向随机微分方程的解.本文主要研究了由倒向随机微分方程生成的非线性期望及其鞅的性质,证明了当生成元g是超线性时的g-上鞅Riesz分解定理.并且指出经典鞅论中的Riesz分解定理和下期望(又称最小期望)对应的上鞅Riesz分解定理是g-上鞅Riesz分解定理的两种特殊情况.  相似文献   

19.
We study a class of reflected backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution are proved by a double penalization approach under regularity assumptions on the obstacle. In a suitable regime switching diffusion framework, we show the connection between our class of BSDEs and fully nonlinear variational inequalities. Our BSDE representation provides in particular a Feynman–Kac type formula for PDEs associated to general zero-sum stochastic differential controller-and-stopper games, where control affects both drift and diffusion term, and the diffusion coefficient can be degenerate. Moreover, we state a dual game formula of this BSDE minimal solution involving equivalent change of probability measures, and discount processes. This gives in particular a new representation for zero-sum stochastic differential controller-and-stopper games.  相似文献   

20.
本文给出了数值求解非线性发展方程的全离散非线性Galerkin算法,即将空间离散时的谱非线性Galerkin算法和时间离散的Euler差分格式相结合,得到了显式和隐式两种全离散数值格式,相应地也考虑了显式和隐式的Galerkin全离散格式,并分别分析了上述四种全离散格式的收敛性和复杂性,经过比较得出结论;在某些约束条件下,非线性Galerkin算法和Galerkin算法具有相同阶的收敛速度,然而前  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号