标题： 关于与收缩半群的相似性和张量积，我 显示英文标题

标题： On similarity to contraction semigroups and tensor products, I

摘要： 在有限希尔伯特空间张量积的背景下，我们证明了算子半群的张量积与收缩半群的相似性等价于每个因子的相应相似性，经过适当的缩放后。 类似的结果在用准收缩性代替收缩性时也成立。 这种分解现象使我们能够构造新的并且在某种意义上是最强的$C_0$-半群例子，这些例子不与收缩相似，从而完成了该理论的重要章节。 我们还讨论了离散情形，并将其与我们的结果联系起来。 显示英文摘要

摘要： In the context of finite tensor products of Hilbert spaces, we prove that similarity of a tensor product of operator semigroups to a contraction semigroup is equivalent to the corresponding similarity for each factor, after an appropriate rescaling. A similar result holds with contractivity replaced by quasi-contractivity. This splitting phenomenon allows us to construct new and, in a sense, the strongest possible examples of $C_0$-semigroups not similar to contractions, thus completing an important chapter of the theory. We also address the discrete setting and relate it to our results.