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
In this paper, we study the extension of isometries between the unit spheres of normed space E and C(Ω). We obtain that any surjective isometry between the unit spheres of normed space E and C(Ω) can be extended...In this paper, we study the extension of isometries between the unit spheres of normed space E and C(Ω). We obtain that any surjective isometry between the unit spheres of normed space E and C(Ω) can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley's problem (where Ω be a compact metric space).展开更多
In this paper we study the isometric extension problem and show that every surjective isometry between the unit spheres of L^p(μ) (1 〈 p 〈∞, p ≠ 2) and a Banach space E can be extended to a linear isometry fr...In this paper we study the isometric extension problem and show that every surjective isometry between the unit spheres of L^p(μ) (1 〈 p 〈∞, p ≠ 2) and a Banach space E can be extended to a linear isometry from L^p(μ) onto E, which means that if the unit sphere of E is (metrically) isometric to the unit sphere of L^P(μ), then E is linearly isometric to L^p(μ). We also prove that every surjective 1-Lipschitz or anti-l-Lipschitz map between the unit spheres of L^p(μ1, H1) and L^p(μ2, H2) must be an isometry and can be extended to a linear isometry from L^p(μ2, H2) to L^p(μ2, H2), where H1 and H2 are Hilbert spaces.展开更多
In this paper, we prove that an into isometry form S(l(n)^∞) to S(E), which under some conditions, can be extended to be a linear isometry defined on the whole space. Therefore we improve the results of [Ding, ...In this paper, we prove that an into isometry form S(l(n)^∞) to S(E), which under some conditions, can be extended to be a linear isometry defined on the whole space. Therefore we improve the results of [Ding, G. G.: The isometric extension of an into mapping from the unit sphere S(l(2)^∞) to S(Lμ^1). Acta Mathematica Sinica, English Series, 22(6), 1721-1724 (2006)].展开更多
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In this paper, we study the extension of isometries between the unit spheres of normed space E and C(Ω). We obtain that any surjective isometry between the unit spheres of normed space E and C(Ω) can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley's problem (where Ω be a compact metric space).
基金Supported by the Fundamental Research Funds for the Central UniversitiesNational Natural Science Foundation of China (Grant No. 10871101)
文摘In this paper we study the isometric extension problem and show that every surjective isometry between the unit spheres of L^p(μ) (1 〈 p 〈∞, p ≠ 2) and a Banach space E can be extended to a linear isometry from L^p(μ) onto E, which means that if the unit sphere of E is (metrically) isometric to the unit sphere of L^P(μ), then E is linearly isometric to L^p(μ). We also prove that every surjective 1-Lipschitz or anti-l-Lipschitz map between the unit spheres of L^p(μ1, H1) and L^p(μ2, H2) must be an isometry and can be extended to a linear isometry from L^p(μ2, H2) to L^p(μ2, H2), where H1 and H2 are Hilbert spaces.
基金Supported by National Natural Science Foundation of China (Grant No. 10871101)the Doctoral Pr0grame Foundation of Institution of Higher Education (Grant No. 20060055010)
文摘In this paper, we prove that an into isometry form S(l(n)^∞) to S(E), which under some conditions, can be extended to be a linear isometry defined on the whole space. Therefore we improve the results of [Ding, G. G.: The isometric extension of an into mapping from the unit sphere S(l(2)^∞) to S(Lμ^1). Acta Mathematica Sinica, English Series, 22(6), 1721-1724 (2006)].