Every non-smooth 2-dimensional Banach space has the Mazur-Ulam property. (English) Zbl 1476.46008
A famous problem of Tingley asks whether every surjective isometry between the unit spheres of two Banach spaces \(X\) and \(Y\) can be extended to a linear isometry between \(X\) and \(Y\). An equivalent formulation reads as follows: does every Banach space \(X\) have the Mazur-Ulam property?
In this paper, the authors show that this is the case for every non-smooth two-dimensional Banach space \(X\).
In a forthcoming work [T. Banakh, “Every 2-dimensional Banach space has the Mazur-Ulam property”, Preprint (2021), arXiv:2103.09268] based on the result of this paper, the first named author proves that indeed every two-dimensional Banach spaces has the Mazur-Ulam property.
In this paper, the authors show that this is the case for every non-smooth two-dimensional Banach space \(X\).
In a forthcoming work [T. Banakh, “Every 2-dimensional Banach space has the Mazur-Ulam property”, Preprint (2021), arXiv:2103.09268] based on the result of this paper, the first named author proves that indeed every two-dimensional Banach spaces has the Mazur-Ulam property.
Reviewer: Jan-David Hardtke (Leipzig)
References:
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