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-semigroup in Hilbert space, then T(t) is similar to a contraction semigroup. Analogously, if T is a power-bounded quasi-compact operator, then T is similar to a contraction. This latter fact is a simultaneous generalization of well known results of Sz.-Nagy and Rota. Some characterizations of bounded quasi-compact semigroups and power-bounded quasi-compact operators are also given.
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Vu, QP., Yao, F. On Similarity to Contraction Semigroups in Hilbert Space. Semigroup Forum 56, 197–204 (1998). https://doi.org/10.1007/PL00005941
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DOI: https://doi.org/10.1007/PL00005941