Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries?
Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries?
复制标题
可以通过由酉集确定的度量空间来识别两个酉 JB* 代数吗？
DOI：
10.1080/03081087.2021.2003745
复制
发表时间：
2021
影响因子：
1.1
通讯作者：
Cueto-Avellaneda M
中科院分区：
文献类型：
--
作者：
Cueto-Avellaneda M
设MandNbe是两个单位代数，让and分别表示MandN中所有单位的集合。我们证明了下列命题是等价的：MandNare等距同构于(复)Banach空间；MandNare等距同构于实Banach空间；存在满射等距.我们实际上建立了一个更一般的命题：在一些温和的额外条件下，对于每个满射等距，我们可以在子集上找到与Δ重合的满射实线性等距.如果我们假设MandNare-代数，则每个满射等距都允许从MontoN到满射实线性等距有一个(唯一的)扩张。这是Hatori-Molnár定理在-代数集上的推广。
LetMandNbe two unital-algebras and letanddenote the sets of all unitaries inMandN, respectively. We prove that the following statements are equivalent:MandNare isometrically isomorphic as (complex) Banach spaces;MandNare isometrically isomorphic as real Banach spaces;there exists a surjective isometry.We actually establish a more general statement asserting that, under some mild extra conditions, for each surjective isometrywe can find a surjective real linear isometrywhich coincides with Δ on the subset. If we assume thatMandNare-algebras, then every surjective isometryadmits a (unique) extension to a surjective real linear isometry fromMontoN. This is an extension of the Hatori–Molnár theorem to the setting of-algebras.