The isometrical extensions of 1-Lipschitz mappings on Gteaux differentiability spaces

Let X and Y be real Banach spaces.Suppose that the subset sm[S1(X)] of the smooth points of the unit sphere [S1(X)] is dense in S1(X).If T0 is a surjective 1-Lipschitz mapping between two unit spheres,then,under some condition,T0 can be extended to a linear isometry on the whole space.     

Blaschke hypersurfaces with symmetric shape operator

A Blaschke hypersurface admits \(\hat \nabla S\) symmetry if and only if \(\hat \nabla S(X,Y) = \hat \nabla S(Y,X)\). We prove that the shape operator has only one eigenvalue. And such Blaschke surfaces are classified as affine spheres or ruled surfaces.     

赋范线性空间上有界线性泛函的一般形式

1968年,N.E.Gretsky求得了Banach函数空间上有界线性泛函的一般形式。1977年,G.D.Faulkner对自反的Banach空间解决了这个问题。又本文作者对一类无限多个Banach空间解决了有界线性泛函的表示问题。 本文对一般的赋范线性空间给出了有界线性泛函的表达式和共轭空间的等距同构表现。     

Regular-Norm Balls can be Closed in the Strong Operator Topology

The main results obtained are:– A Dedekind complete Banach lattice Y has a Fatou norm if and only if, for any Banach lattice X, the regular-norm unit ball Ur = {T Lr(X,Y): ||T||r 1} is closed in the strong operator topology on the space of all regular operators, Lr(X,Y).– A Dedekind complete Banach lattice Y has a norm which is both Fatou and Levi if and only if, for any Banach lattice X, the regular-norm unit ball Ur is closed in the strong operator topology on the space of all bounded operators, L(X,Y).– A Banach lattice Y has a Fatou–Levi norm if and only if for every L-space X the space L(X,Y) is a Banach lattice under the operator norm.– A Banach lattice Y is isometrically order isomorphic to C(S) with the supremum norm, for some Stonean space S, if and only if, for every Banach lattice X, L(X,Y) is a Banach lattice under the operator norm.Several examples demonstrating that the hypotheses may not be removed, as well as some applications of the results obtained to the spaces of operators are also given. For instance:– If X = Lp() and Y = Lq(), where 1 < p,q < , then Lr(X,Y) is a first category subset of L(X,Y).     

套链分解

Let X1,X2,...,Xk be k disjoint subsets of S with the same cardinality m.Define H(m,k) = {X (C) S: X (C) Xi for 1 ≤I ≤k} and P(m,k) = {X (C) S : X ∩ Xi ≠φ for at least two Xi's}.Suppose S = Uki=1 Xi,and let Q(m,k,2) be the collection of all subsets K of S satisfying|K ∩ Xi|≥ 2 for some 1 ≤ I ≤ k.For any two disjoint subsets Y1 and Y2 of S,we define F1,j = {X (C) S : either |X ∩ Y1|≥ 1 or |X ∩ Y2|≥ j}.It is obvious that the four posers are graded posets ordered by inclusion.In this paper we will prove that the four posets are nested chain orders.     

关于球面的紧子流形

本文讨论单位球面的紧致子流形的Pinching问题.改进了S.T.Yan与莫小欢有关球面中具有平行平均曲率的紧致子流形的Pinching常数及S.S.Chern等与沈一兵有关紧致极小子流形的Pinching常数.对截曲率的情形,本文还改进了沈一兵有关截曲率的Pinching常数.     

Topological continuous convergence

Let X be a limit space, Y a topological space. We show that c(X,Y), the limitierung of continuous convergence on LIM(X,Y), is topological whenever X is basic locally compact. For regular Y, local compactness of X is sufficient. In both cases, c(X,Y) coincides with the compact-open topology. If X satisfies a certain regularity condition, the fact that c(X,Y) is topological implies, conversely, that X is (basic) locally compact.The author would like to thank S. Weck for some inspiring discussions.     

Asymptotically Isometric Copy of lβ (0 ＜β ＜ 1) in Spaces of Bounded Linear Operators

Assume X is a normed space, every x* ∈ S(X*) can reach its norm at some point in B(X), and Y is a β-normed space. If there is a quotient space of Y which is asymptotically isometric to lβ, then L(X, Y) contains an asymptotically isometric copy of lβ. Some sufficient conditions are given under which L(X, Y) fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L(X, Y).     

单位球面上的等距扩张

本文讨论了Ｌ１（Ω，Ｘ）的子空间上的单位球面等距扩张问题．在一定条件下，给出对此问题肯定的回答．     

使决策单元变为DEA有效的偏差和最小法

某决策单元为非 DEA有效 ( C2 R或 C2 GS2 ) ,为了将它变为 DEA有效 ,在找出其对应点附近的一些有效前沿面的基础上 ,给出了使其对应点与这些有效前沿面上的点的输入、输出的偏差和最小的方法 .     

夹心半群S(X,Y,θ)上的α-同余

本文讨论了夹心半群T(X,Y,θ)上的α-同余与集合Y上Tθ-等价关系之间的联系,证明了对于每个Tθ-等价关系E,夹心半群同余格C(T(X,Y,θ))的完全子格γ-1(E)中的最大元是一个α-同余,并判明Symons同余l,d都是α-同余.对于某些拓扑空间X,Y,确定了夹心半群S(X,Y,θ)上的最小(最大)真α-同余.     

严格凸、光滑、自反的Banach空间中等距映射的线性延拓

本文主要研究了任意两个严格凸,光滑的自反空间E,F的单位球面S(E)和S(F)之间任意等距映射的线性延拓问题.     

Identification of some real interpolation spaces

We interrelate the real interpolation spaces associated with the couples , and , proving among others the identities

for all .

     

JOINT SPECTRAL SETS

Abstract

We consider the problem: if S,TEB(H) are commuting operators with von Neumann spectral sets X and Y respectively, does it imply that X x Y is a joint spectral set for the pair (S,T)?     

加权经验累计分位函数的弱收敛

记(X,Y)为二元随机变量,F(x)为X的边缘分布函数.定义Y关于X的分位回归函数为h(u)=E(Y|F(X)=u),记S(u)=∫u0J(t)h(t)dt为加权累计分位回归函数,其中J(@)为权函数.本文讨论了S(u)的经验版本的弱收敛性质.     

Stability Characterizations of ε-isometries on Certain Banach Spaces

Suppose that X, Y are two real Banach Spaces. We know that for a standard ε-isometry f : X → Y, the weak stability formula holds and by applying the formula we can induce a closed subspace N of *. In this paper, by using again the weak stability formula, we further show a sufficient and necessary condition for a standard ε-isometry to be stable in assuming that N is w*-closed in Y*.Making use of this result, we improve several known results including Figiel's theorem in reflexive spaces.We also prove that if, in addition, the space Y is quasi-reflexive and hereditarily indecomposable, then L(f)≡span[f(X)] contains a complemented linear isometric copy of X; Moreover, if X =Y, then for every e-isometry f: X → X, there exists a surjective linear isometry S:X → X such that f-S is uniformly bounded by 2ε on X.     

A solution to Tingley’s problem for isometries between the unit spheres of compact C*-algebras and JB*-triples

Let f : S(E) → S(B) be a surjective isometry between the unit spheres of two weakly compact JB*-triples not containing direct summands of rank less than or equal to 3. Suppose E has rank greater than or equal to 5. Applying techniques developed in JB*-triple theory, we prove that f admits an extension to a surjective real linear isometry T : E → B. Among the consequences, we show that every surjective isometry between the unit spheres of two compact C*-algebras A and B, without assuming any restriction on the rank of their direct summands(and in particular when A = K(H) and B = K(H′)), extends to a surjective real linear isometry from A into B. These results provide new examples of infinite-dimensional Banach spaces where Tingley's problem admits a positive answer.     

关于k-消去二分图的一些结果

图 G的一个 k-正则支撑子图称为 G的 k-因子 ,若对 G的任一边 e,图 G- e总存在一个 k-因子 ,则称 G是 k-消去图 .证明了二分图 G=( X,Y) ,且 | X | =| Y|是 k-消去图的充分必要条件是 k| S|≤ r1 + 2 r2 +…+ k( rk+… + rΔ) - ε( S)对所有 S X成立 .并由此给出二分图是 k-消去图的充分度条件 .     

復式乘積和球面乘積的關係

<正> 1.設X為一拓撲空間,以a_i表示X的n_i次同偷羣∏_(ni)(X)的一個元素.在球面乘積S~(n1)×…×S~(nr)中,最高次元的腔胞記為e~(n1+…+nr).在S~(n1)×…×S~(nr)中除去e~(n1+…+nr)而得一空間Y.設S~(nl)為nl次元球,為了印刷方便起見,把S~(nl)記作S(nl).在S(ni)中取一參考點x_i~o.設i_1相似文献   

包含$l^{\beta}(0<\beta<1)$渐近等距翻版的有界线性算子空间

Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.