论文标题
Tingley对不满足Hausdorff距离条件的复杂Banach空间的问题
Tingley's problem for complex Banach spaces which do not satisfy the Hausdorff distance condition
论文作者
论文摘要
在2022年，Hatori为复杂的Banach空间提供了足够的条件。在本文中，我们介绍了一类复杂的Banach空间$ B $，这些$ B $不满足该条件，但享受了此类$ B $的单位球体上的每个溢流等轴测图，该属性承认在整个空间$ b $上延伸到过冲的真实线性等轴测图。本说明中研究的BANACH空间的典型示例是所有Lipschitz复合功能的空间$ {\ rm lip}（[0,1]）$ $ [0,1] $和$ c^1（[0,1]）$的所有连续不同的复杂功能的$ [0,1]）$ [0,1] $ [0,1] $ [0,1] $ | f（0）|+\ | f'\ | _ \ infty $。
In 2022, Hatori gave a sufficient condition for complex Banach spaces to have the complex Mazur--Ulam property. In this paper, we introduce a class of complex Banach spaces $B$ that do not satisfy the condition but enjoy the property that every surjective isometry on the unit sphere of such $B$ admits an extension to a surjective real linear isometry on the whole space $B$. Typical examples of Banach spaces studied in this note are the spaces ${\rm Lip}([0,1])$ of all Lipschitz complex-valued functions on $[0,1]$ and $C^1([0,1])$ of all continuously differentiable complex-valued functions on $[0,1]$ equipped with the norm $|f(0)|+\|f'\|_\infty$.
