论文标题
每一个交换性JB $^*$ - 三重都满足复杂的Mazur - Ulam属性
Every commutative JB$^*$-triple satisfies the complex Mazur--Ulam property
论文作者
论文摘要
我们证明，每一个交换性JB $^*$ - 三重都可以满足复杂的Mazur- ulam属性。多亏了代表理论，我们可以确定交换性的JB $^*$ - 将复杂值的连续功能的空间作为主体$ \ Mathbb {t} $ - bundle $ l $ y Mathbb {t} $ l $中的$ c_0^\ mathbb {t}（t}（T） （λ，t）\ in \ mathbb {t} \ times l \}。$$我们证明，从$ C_0^\ Mathbb {t}（l）$的单位球体中的每个过滤式等轴测图上的任何一个复杂的Banach空间的单位球体都延伸至空间之间的冲流真实的线性等值线。
We prove that every commutative JB$^*$-triple satisfies the complex Mazur--Ulam property. Thanks to the representation theory, we can identify commutative JB$^*$-triples as spaces of complex-valued continuous functions on a principal $\mathbb{T}$-bundle $L$ in the form $$C_0^\mathbb{T}(L):=\{a\in C_0(L):a(λt)=λa(t)\text{ for every } (λ,t)\in\mathbb{T}\times L\}.$$ We prove that every surjective isometry from the unit sphere of $C_0^\mathbb{T}(L)$ onto the unit sphere of any complex Banach space admits an extension to a surjective real linear isometry between the spaces.
