References
- Ding GG . The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space. Sci China Ser A. 2002;45(4):479–483.
- Ding GG . The isometric extension problem in the spheres of lp(γ) (p > 1) type spaces. Sci China Ser A. 2003;46:333–338.
- Ding GG . On the extension of isometries between unit spheres of E and C(Ω). Acta Math Sin (Engl Ser.). 2003;19:793–800.
- Ding GG . The representation theorem of onto isometric mappings between two unit spheres of l∞-type spaces and the application on isometric extension problem. Sci China Ser A. 2004;47:722–729.
- Ding GG . The representation theorem of onto isometric mappings between two unit spheres of l1(γ) type spaces and the application to the isometric extension problem. Acta Math Sin (Engl Ser.). 2004;20:1089–1094.
- Ding GG . The isometric extension of the into mapping from a ℒ∞ (γ)-type space to some Banach space. Illinois J Math. 2007;51(2):445–453.
- Li L , Ren W . On extension of isometries between unit spheres of ℒ∞ and E. Quaest Math. 2008;31(3):209–218.
- Liu R . On extension of isometries between unit spheres of ℒ∞ (γ)-type space and a Banach space E. J Math Anal Appl. 2007;333:959–970.
- Kadets V , Martín M . Extension of isometries between unit spheres of infinite-dimensional polyhedral Banach spaces. J Math Anal Appl. 2012;396:441–447.
- Wang RS . Isometries between the unit spheres of C0(Ω) type spaces. Acta Math Sci (Engl Ed.). 1994;14(1):82–89.
- Tanaka R . Spherical isometries of finite dimensional C*-algebras. J Math Anal Appl. 2017;445(1):337–341.
- Tanaka R . The solution of Tingley’s problem for the operator norm unit sphere of complex n × n matrices. Linear Algebra Appl. 2016;494:274–285.
- Tanaka R . Tingley’s problem on finite von Neumann algebras. J Math Anal Appl. 2017;451:319–326.
- Peralta AM , Tanaka R . A solution to Tingley’s problem for isometries between the unit spheres of compact C*-algebras and JB*-triples. Sci China Math. Forthcoming. arXiv:1608.06327v1.
- Fernández-Polo FJ , Peralta AM . Low rank compact operators and Tingley’s problem, preprint 2016. arXiv:1611.10218v1.
- Fernández-Polo FJ , Peralta AM . On the extension of isometries between the unit spheres of a C*-algebra and B(H). Trans Amer Math Soc. Forthcoming. arXiv:1701.02916v1.
- Fernández-Polo FJ , Peralta AM . Tingley’s problem through the facial structure of an atomic JBW*-triple. J Math Anal Appl. 2017;455(1):750–760.
- Fernández-Polo FJ , Garcés JJ , Peralta AM , et al . Tingley’s problem for spaces of trace class operators. Linear Algebra Appl. 2017;529:294–323.
- Cheng L , Dong Y . On a generalized Mazur-Ulam question: extension of isometries between unit spheres of Banach spaces. J Math Anal Appl. 2011;377:464–470.
- Fang XN , Wang JH . Extension of isometries between the unit spheres of normed space E and C(Ω). Acta Math Sin (Engl Ser.). 2006;22:1819–1824.
- Tan D . On extension of isometries on the unit spheres of L∞-spaces for 0 < p ≤ 1. Nonlinear Anal. 2011;74:6981–6987.
- Tan D . Extension of isometries on unit sphere of L∞ . Taiwanese J Math. 2011;15:819–827.
- Tan D . Extension of isometries on the unit sphere of Lp-spaces. Acta Math Sin (Engl Ser.). 2012;28:1197–1208.
- Li JZ . Mazur-Ulam property of the sum of two strictly convex Banach spaces. Bull Aust Math Soc. 2016;93(3):473–485.
- Tan D , Huang X , Liu R . Generalized-lush spaces and the Mazur-Ulam property. Studia Math. 2013;219:139–153.
- Tan D , Liu R . A note on the Mazur-Ulam property of almost-CL-spaces. J Math Anal Appl. 2013;405:336–341.
- Tanaka R . A further property of spherical isometries. Bull Aust Math Soc. 2014;90:304–310.
- Megginson RE . An introduction to Banach space theory. New York (NY): Springer-Verlag; 1998.
- Tingley D . Isometries of the unit sphere. Geom Dedicata. 1987;22:371–378.
- Oikhberg T , Peralta AM , Ramírez M . Automatic continuity of M-norms on C*-algebras. J Math Anal Appl. 2011;381:799–811.
- Peralta AM . Extending surjective isometries defined on the unit sphere of l∞ (γ), preprint 2017. arXiv:1709.09584v1.