On similarity to contraction semigroups and tensor products, I

Oliva-Maza, J. (Universidad de Zaragoza) ; Tomilov, Y.

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.jfa.2026.111492

Año: 2026

Publicado en: JOURNAL OF FUNCTIONAL ANALYSIS (2026), 111492 [37 pp.]
ISSN: 0022-1236

Financiación: info:eu-repo/grantAgreement/ES/AEI/AEI PID2022-137294NB-I00
Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R

Tipo y forma: Article (Published version)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)