In this paper,we study Tingley＇s problem on symmetric absolute normalized norms on R^2.We construct new methods for Tingley＇s problem on two-dimensional spaces by using isosceles orthogonality,which does not make us...In this paper,we study Tingley＇s problem on symmetric absolute normalized norms on R^2.We construct new methods for Tingley＇s problem on two-dimensional spaces by using isosceles orthogonality,which does not make use of the notion of natural extension.Furthermore,using our methods,several sufficient conditions for Tingley＇s problem on symmetric absolute normalized norms on R2 are given.As applications,we present various new examples including the two-dimensional Lorentz sequence space d^（2）（ω,q） and its dual d^（2）（ω,q）＊by simple arguments.展开更多
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. A...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.展开更多
文章得到以下结果(它改进了文献[16][18]中的一些结果):设E是一个赋范空间,V0是单位球面S(Lp(Γ,Σ,μ))到单位球面S(E)内的等距映射。如果V0满足下列两个条件:(ⅰ)对于任意的自然数n,实数ξk∈[-1,1]及χAk∈χ(Γ),1≤k≤n,有‖sum fr...文章得到以下结果(它改进了文献[16][18]中的一些结果):设E是一个赋范空间,V0是单位球面S(Lp(Γ,Σ,μ))到单位球面S(E)内的等距映射。如果V0满足下列两个条件:(ⅰ)对于任意的自然数n,实数ξk∈[-1,1]及χAk∈χ(Γ),1≤k≤n,有‖sum from k=1 to n ξkμ(Ai)1/pV0〔(χAi)/(μ(Ai)1/p)〕‖p=sum from k=1 to n|ξk|pμ(Ai),(ⅱ)对于任意的f1,f2∈S(Lp(Γ,Σ,μ))和实数ξ1,ξ2∈[-1,1],有‖ξ1V0(f1)+ξ2V0(f2)‖=1|ξ1V0(f1)+ξ2V0(f2)∈V0[S(Lp(Γ,Σ,μ)],那么V0可延拓为全空间Lp(Γ,Σ,μ)上的等距线性算子。展开更多
In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry ...In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole space.展开更多
In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.
文摘In this paper,we study Tingley＇s problem on symmetric absolute normalized norms on R^2.We construct new methods for Tingley＇s problem on two-dimensional spaces by using isosceles orthogonality,which does not make use of the notion of natural extension.Furthermore,using our methods,several sufficient conditions for Tingley＇s problem on symmetric absolute normalized norms on R2 are given.As applications,we present various new examples including the two-dimensional Lorentz sequence space d^（2）（ω,q） and its dual d^（2）（ω,q）＊by simple arguments.
基金supported by the Spanish Ministry of Economy and Competitiveness and European Regional Development Fund (Grant No. MTM2014-58984-P)Junta de Andalucía (Grant No. FQM375)+1 种基金Grants-in-Aid for Scientific Research (Grant No. 16J01162)Japan Society for the Promotion of Science
文摘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.
文摘文章得到以下结果(它改进了文献[16][18]中的一些结果):设E是一个赋范空间,V0是单位球面S(Lp(Γ,Σ,μ))到单位球面S(E)内的等距映射。如果V0满足下列两个条件:(ⅰ)对于任意的自然数n,实数ξk∈[-1,1]及χAk∈χ(Γ),1≤k≤n,有‖sum from k=1 to n ξkμ(Ai)1/pV0〔(χAi)/(μ(Ai)1/p)〕‖p=sum from k=1 to n|ξk|pμ(Ai),(ⅱ)对于任意的f1,f2∈S(Lp(Γ,Σ,μ))和实数ξ1,ξ2∈[-1,1],有‖ξ1V0(f1)+ξ2V0(f2)‖=1|ξ1V0(f1)+ξ2V0(f2)∈V0[S(Lp(Γ,Σ,μ)],那么V0可延拓为全空间Lp(Γ,Σ,μ)上的等距线性算子。
基金Supported by NSFC (10871101)the Doctoral Programme Foundation of Institution of Higher Education (20060055010)
文摘In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole space.
文摘In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.
