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81.
Ngaiming Mok 《中国科学A辑(英文版)》2008,51(4):660-684
In 1993,Tsal proved that a proper holomorphic mapping f:Ω→Ω' from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domainΩ' is necessarily totally geodesic provided that r':=rank(Ω')≤rank(Ω):= r,proving a conjecture of the author's motivated by Hermitian metric rigidity.As a first step in the proof,Tsai showed that df preserves almost everywhere the set of tangent vectors of rank 1.Identifying bounded symmetric domains as open subsets of their compact duals by means of the Borel embedding,this means that the germ of f at a general point preserves the varieties of minimal rational tangents(VMRTs). In another completely different direction Hwang-Mok established with very few exceptions the Cartan- Fubini extension priniciple for germs of local biholomorphisms between Fano manifolds of Picard num- ber 1,showing that the germ of map extends to a global biholomorphism provided that it preserves VMRTs.We propose to isolate the problem of characterization of special holomorphic embeddings between Fano manifolds of Picard number 1,especially in the case of classical manifolds such as ratio- nal homogeneous spaces of Picard number 1,by a non-equidimensional analogue of the Cartan-Fubini extension principle.As an illustration we show along this line that standard embeddings between com- plex Grassmann manifolds of rank≤2 can be characterized by the VMRT-preserving property and a non-degeneracy condition,giving a new proof of a result of Neretin's which on the one hand paves the way for far-reaching generalizations to the context of rational homogeneous spaces and more generally Fano manifolds of Picard number 1,on the other hand should be applicable to the study of proper holomorphic mappings between bounded domains carrying some form of geometric structures. 相似文献
82.
Chi-Kwong Li Yiu-Tung Poon Nung-Sing Sze 《Proceedings of the American Mathematical Society》2005,133(2):369-377
We characterize linear maps between different rectangular matrix spaces preserving Ky Fan norms.
83.
It is shown that an n × n matrix of continuous linear maps from a pro-C^*-algebra A to L(H), which verifies the condition of complete positivity, is of the form [V^*TijФ(·)V]^n i,where Ф is a representation of A on a Hilbert space K, V is a bounded linear operator from H to K, and j=1,[Tij]^n i,j=1 is a positive element in the C^*-algebra of all n×n matrices over the commutant of Ф(A) in L(K). This generalizes a result of C. Y.Suen in Proc. Amer. Math. Soc., 112(3), 1991, 709-712. Also, a covariant version of this construction is given. 相似文献
84.
Dennis Kretschmann Dirk Schlingemann Reinhard F. Werner 《Journal of Functional Analysis》2008,255(8):1889-1904
We show a continuity theorem for Stinespring's dilation: two completely positive maps between arbitrary C∗-algebras are close in cb-norm if and only if we can find corresponding dilations that are close in operator norm. The proof establishes the equivalence of the cb-norm distance and the Bures distance for completely positive maps. We briefly discuss applications to quantum information theory. 相似文献
85.
86.
Common fixed point results for noncommuting mappings without continuity in cone metric spaces 总被引:1,自引:0,他引:1
The existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions, without appealing to continuity, in a cone metric space is established. These results generalize several well-known comparable results in the literature. 相似文献
87.
88.
传统的基于形状信息目标定位的算法,对目标观测角度发生形变情况下的定位存在不少困难,针对该问题,提出了一种基于稀疏活动轮廓模型的感兴趣目标(OOI)检测算法.首先通过共同勾画算法学习到感兴趣目标的稀疏活动轮廓模型,它能够清晰地定义感兴趣目标模式;同时构成该模型的Gabor轮廓基元可以通过扰动进行局部的调整以适配图像,在一... 相似文献
89.
We show that the equality m1(f(x))=m2(g(x)) for x in a neighborhood of a point a remains valid for all x provided that f and g are open holomorphic maps, f(a)=g(a)=0 and m1,m2 are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between f and g is obtained. 相似文献
90.
The present paper contains a martingale representation theorem for set-valued martingales defined on a filtered probability space with a filtration generated by a Brownian motion. It is proved that such type martingales can be defined by some generalized set-valued stochastic integrals with respect to a given Brownian motion. The main result of the paper is preceded by short part devoted to the definition and some properties of generalized set-valued stochastic integrals. 相似文献