caa a22 4500 388092572 CHVBK 20180307125255.0 cr unu---uuuuu 161130e199912 xx s 000 0 eng 10.1017/S0004972700036613 doi S0004972700036613 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700036613 Simard Arnaud Equipe de Mathématiques de Basançon Université de Franche-Comté 25030 Besancon cedex France, e-mail: simard@math.univ-fcomte.fr Counterexamples concerning powers of sectorial operators on a Hilbert space [Elektronische Daten] [Arnaud Simard] We give explicit constructions of semigroups and operators with particular properties. First we build a bounded C0-semigroup which is invertible and which is not similar to a semigroup of contractions. Afterwards we exhibit operators which admit bounded imaginary powers of angle ω > 0 on a Hilbert space but which do not admit a bounded functional calculus on the sector of angle ω. (This gives the limit of McIntosh's fundamental result.) Finally we build, in the 2-dimensional Hilbert space, an operator which is not the negative generator of a semigroup of contractions, although its imaginary powers are bounded by eπ|s|/2. Copyright © Australian Mathematical Society 1999 Bulletin of the Australian Mathematical Society Cambridge University Press 60/3(1999-12), 459-468 0004-9727 60:3<459 1999 60 BAZ https://doi.org/10.1017/S0004972700036613 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700036613 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Simard Arnaud Equipe de Mathématiques de Basançon Université de Franche-Comté 25030 Besancon cedex France, e-mail: simard@math.univ-fcomte.fr NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/3(1999-12), 459-468 0004-9727 60:3<459 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge