Under the condition that the unit ball has sufficiently many extreme points, every 2-local nonlinear surjective isometry on a normed space is affine.
2-local isometries on function spaces
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abstract
We study 2-local reflexivity of the set of all surjective isometries between certain function spaces. We do not assume linearity for isometries. We prove that a 2-local isometry in the group of all surjective isometries on the algebra of all continuously differentiable functions on the closed unit interval with respect to several norms is a surjective isometry. We also prove that a 2-local isometry in the group of all surjective isometries on the Banach algebra of all Lipschitz functions on the closed unit interval with the sum-norm is a surjective isometry.
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math.FA 2years
2019 2verdicts
UNVERDICTED 2representative citing papers
2-local *-automorphisms of B(H) for separable H are *-automorphisms when the two defining equations are compressed into one.
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On 2-local nonlinear surjective isometries on normed spaces and C$^*$-algebras
Under the condition that the unit ball has sufficiently many extreme points, every 2-local nonlinear surjective isometry on a normed space is affine.
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On 2-local *-automorphisms and 2-local isometries of B(H)
2-local *-automorphisms of B(H) for separable H are *-automorphisms when the two defining equations are compressed into one.