论文标题
JB $^*$ - 代数的正交性保存器的单参数组
One-parameter groups of orthogonality preservers on JB$^*$-algebras
论文作者
论文摘要
在第一个目标中，我们提高了对溢流和界限有限的线性操作员的理解，从JB $^*$ - 代数$ \ Mathcal {a} $保存正交性到JB $^*$ - TRIPLE $ E $。在许多其他结论中，还表明，有界的线性两组式$ t：\ Mathcal {a} \ to e $是正交性保留的，并且只有在保留的情况下，只有在两个方向上保存零triple-triple-propoductss in Directions（即，即保留零triple productions）（即） \ {t（a），t（b），t（c）\} = 0 $）。在第二个主要结果中，我们建立了所有单参数组在JB $^*$ - 代数上保存操作员的完整表征。
In a first objective we improve our understanding about surjective and bijective bounded linear operators preserving orthogonality from a JB$^*$-algebra $\mathcal{A}$ into a JB$^*$-triple $E$. Among many other conclusions, it is shown that a bounded linear bijection $T: \mathcal{A}\to E$ is orthogonality preserving if, and only if, it is biorthogonality preserving if, and only if, it preserves zero-triple-products in both directions (i.e., $\{a,b,c\}=0 \Leftrightarrow \{T(a),T(b),T(c)\}=0$). In the second main result we establish a complete characterization of all one-parameter groups of orthogonality preserving operators on a JB$^*$-algebra.
