2-Local Isometries on Spaces of Lipschitz Functions
2011 ◽
Vol 54
(4)
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pp. 680-692
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Keyword(s):
AbstractLet (X, d) be a metric space, and let Lip(X) denote the Banach space of all scalar-valued bounded Lipschitz functions ƒ on X endowed with one of the natural normswhere L(ƒ) is the Lipschitz constant of ƒ. It is said that the isometry group of Lip(X) is canonical if every surjective linear isometry of Lip(X) is induced by a surjective isometry of X. In this paper we prove that if X is bounded separable and the isometry group of Lip(X) is canonical, then every 2-local isometry of Lip(X) is a surjective linear isometry. Furthermore, we give a complete description of all 2-local isometries of Lip(X) when X is bounded.
1968 ◽
Vol 20
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pp. 1150-1164
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1992 ◽
Vol 34
(1)
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pp. 1-9
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2014 ◽
Vol 58
(3)
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pp. 631-636
2019 ◽
pp. 1-27
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1979 ◽
Vol 85
(2)
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pp. 317-324
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1987 ◽
Vol 105
(1)
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pp. 117-126
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2000 ◽
Vol 43
(3)
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pp. 511-528
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2017 ◽
Vol 165
(3)
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pp. 467-473
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