论文标题
部分可观测时空混沌系统的无模型预测
Maps preserving triple transition pseudo-probabilities
论文作者
论文摘要
让$ e $和$ v $是JBW $^*$ - 三重$ m $中的最小三胞胎。我们介绍了从$ e $到$ v $的三重过渡伪概率的概念，因为复数数字$ ttp（e，v）=φ_v（e），$ $φ_v$是$ m _*$的封闭式单位球的独特极端点，$ m _*$，$ v $ n n n n n un n n n un n n n un n n n n un n n n n n un n n n an n un n n n n n n n n an n un-Forment an n un-Formant n n n n n n n n an n un Nords。在von Neumann代数中的两个最小投影的情况下，这与通常的过渡概率相对应。 We prove that every bijective transformation $Φ$ preserving triple transition pseudo-probabilities between the lattices of tripotents of two atomic JBW$^*$-triples $M$ and $N$ admits an extension to a bijective {\rm(}complex{\rm)} linear mapping between the socles of these JBW$^*$-triples.如果我们还假设$φ$保留正交性，则$φ$可以将其扩展到汇总（复杂 - ）线性{\ rm（}等值{\ rm）} $ m $ $ m $的三份同构。如果$ m $和$ n $是两个旋转因素或两个型1型cartan因素，我们通过在保存器上的技术和结果表明，每个双线都保留了三重过渡伪探针之间的三重伪探针，$ m $和$ n $和$ n $的晶格自动保存了ofthe use $ $ uso $ $ $ $ $ n $ $ n $ n $ n $ n $ n $ n $。
Let $e$ and $v$ be minimal tripotents in a JBW$^*$-triple $M$. We introduce the notion of triple transition pseudo-probability from $e$ to $v$ as the complex number $TTP(e,v)= φ_v(e),$ where $φ_v$ is the unique extreme point of the closed unit ball of $M_*$ at which $v$ attains its norm. In the case of two minimal projections in a von Neumann algebra, this correspond to the usual transition probability. We prove that every bijective transformation $Φ$ preserving triple transition pseudo-probabilities between the lattices of tripotents of two atomic JBW$^*$-triples $M$ and $N$ admits an extension to a bijective {\rm(}complex{\rm)} linear mapping between the socles of these JBW$^*$-triples. If we additionally assume that $Φ$ preserves orthogonality, then $Φ$ can be extended to a surjective (complex-)linear {\rm(}isometric{\rm)} triple isomorphism from $M$ onto $N$. In case that $M$ and $N$ are two spin factors or two type 1 Cartan factors we show, via techniques and results on preservers, that every bijection preserving triple transition pseudo-probabilities between the lattices of tripotents of $M$ and $N$ automatically preserves orthogonality, and hence admits an extension to a triple isomorphism from $M$ onto $N$.
