论文标题
与正交性保存器和汇总等法有关的三重过渡伪探针的保留剂
Preservers of triple transition pseudo-probabilities in connection with orthogonality preservers and surjective isometries
论文作者
论文摘要
我们证明，在两个原子JBW $^*$的最小三环体之间，每个双线都保留三重过渡伪探针，这两个方向都会在两个方向上保持正交性。因此，在两个原子JBW $^*$的最小三重动物集之间保留每个三重过渡的伪探针，这恰恰是对相应的JBW $^*$ - 三重三态之间（复杂）线性三倍异态性的限制。该结果可以被视为在$ b（h）$中最小预测上的wigner对称性的著名Wigner定理的三个版本。我们还通过证明了两个原子JBW $^*$ - 三倍的三倍延伸到这两个JBW $^*$ - 三倍的三倍之间，我们还提供了一个Tingley类型定理。我们还表明，在两个原子JBW $^*$ - 三倍的三个最小三重动物集之间的过冲等法相比，通常比保留三重过渡伪验证的两组都宽。
We prove that every bijection preserving triple transition pseudo-probabilities between the sets of minimal tripotents of two atomic JBW$^*$-triples automatically preserves orthogonality in both directions. Consequently, each bijection preserving triple transition pseudo-probabilities between the sets of minimal tripotents of two atomic JBW$^*$-triples is precisely the restriction of a (complex-)linear triple isomorphism between the corresponding JBW$^*$-triples. This result can be regarded as triple version of the celebrated Wigner theorem for Wigner symmetries on the posets of minimal projections in $B(H)$. We also present a Tingley type theorem by proving that every surjective isometry between the sets of minimal tripotents in two atomic JBW$^*$-triples admits an extension to a real linear surjective isometry between these two JBW$^*$-triples. We also show that the class of surjective isometries between the sets of minimal tripotents in two atomic JBW$^*$-triples is, in general, strictly wider than the set of bijections preserving triple transition pseudo-probabilities.
