论文标题
关于伸出的异构体的扩展，其域是紧凑型操作员空间的单位球
On the extension of surjective isometries whose domain is the unit sphere of a space of compact operators
论文作者
论文摘要
我们证明，从空间$ k（h）的单位球体，所有紧凑型运算符的$ $ hilbert space $ h $上的$ $ h $都可以扩展到任意实际的banach space $ y $的单位球，可以将所有紧凑型操作员的$扩展到$ y $ y $。这可能是无限维度非交通c $^*$的第一个示例 - 代数不包含单位和满足Mazur-ulam属性。我们还证明，所有紧凑型C $^*$ - 代数和弱紧凑的JB $^*$ - 三元组都满足Mazur-ulam属性。
We prove that every surjective isometry from the unit sphere of the space $K(H),$ of all compact operators on an arbitrary complex Hilbert space $H$, onto the unit sphere of an arbitrary real Banach space $Y$ can be extended to a surjective real linear isometry from $K(H)$ onto $Y$. This is probably the first example of an infinite dimensional non-commutative C$^*$-algebra containing no unitaries and satisfying the Mazur--Ulam property. We also prove that all compact C$^*$-algebras and all weakly compact JB$^*$-triples satisfy the Mazur--Ulam property.
