On quasi-contractivity of C 0-semigroups on Banach spaces

Matolcsi, Máté (2004) On quasi-contractivity of C 0-semigroups on Banach spaces. ARCHIV DER MATHEMATIK, 83 (4). pp. 360-363. ISSN 0003-889X

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Abstract

A basic result in semigroup theory states that every C-0-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the convergence of the Trotter-type formula (e(t/n) (A) p)(n) (where P denotes a bounded projection), we prove that whenever the generator A is unbounded it is possible to introduce an equivalent norm on the space with respect to which the semigroup is not quasi-contractive.

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