The Lipschitz isomorphism problem asks whether Banach spaces related by a surjective bi-Lipschitz map must be linearly isomorphic. The separable formulation imposes separability on both spaces. A linear isomorphism is a bounded linear bijection with bounded inverse, whereas a Lipschitz isomorphism need not be linear.
Lipschitz Isomorphism Problem
See also
Banach Space, Bi-Lipschitz Map, c0 Space, Separable SpaceExplore with Wolfram|Alpha
References
Godefroy, G. and Kalton, N. J. "Lipschitz-Free Banach Spaces." Studia Math. 159, 121-141, 2003. https://doi.org/10.4064/sm159-1-6.Godefroy, G.; Kalton, N. J.; and Lancien, G. "Subspaces of
and Lipschitz Isomorphisms." Geom. Funct. Anal. 10,
798-820, 2000. https://doi.org/10.1007/PL00001638.
Cite this as:
Weisstein, Eric W. "Lipschitz Isomorphism Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LipschitzIsomorphismProblem.html