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arXiv · 2509.01005

On similarity to contraction semigroups and tensor products, I

J. Oliva-Maza·Y. Tomilov
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Abstract

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.

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J. Oliva-Maza, Y. Tomilov. 2025-08-31. On similarity to contraction semigroups and tensor products, I. https://arxiv.org/abs/2509.01005

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