The problem of characterizing GKLS-generators and CP-maps with an invariant von Neumann algebra ${𝒜}$ appeared in different guises in the literature. We prove two unifying results, which hold even for weakly closed *-algebras: first, we show how to construct a normal form for ${𝒜}$-invariant GKLS-generators, if a normal form for ${𝒜}$-invariant CP-maps is known — rendering the two problems essentially equivalent. Second, we provide a normal form for ${𝒜}$-invariant CP-maps if ${𝒜}$ is atomic (which includes the finite-dimensional case). As an application we reproduce several results from the literature as direct consequences of our characterizations and thereby point out connections between different fields.

用不变的冯诺依曼代数表征 GKLS 生成器和 CP 映射的问题${𝒜}$以不同的形式出现在文学作品中。我们证明了两个统一的结果，即使对于弱闭*-代数也成立：首先，我们展示了如何构造一个范式${𝒜}$-不变的 GKLS 生成器，如果是${𝒜}$-不变的 CP-maps 是已知的——使这两个问题本质上是等价的。其次，我们为${𝒜}$-不变的 CP 映射如果${𝒜}$是原子的（包括有限维的情况）。作为一个应用程序，我们从文献中重现了几个结果作为我们表征的直接结果，从而指出了不同领域之间的联系。