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VOL. 41 | 2003 Similarities of $\omega$-accretive operators
Christian Le Merdy

Editor(s) Xuan Thinh Duong, Alan Pryde


Given a number $0 \lt \omega \leq \frac{\pi}{2}$, an $\omega$-accretive operator is a sectorial operator $A$ on Hilbert space whose numerical range lies in the closed sector of all $z \in \mathbbC$ such that $\vert Arg(z)\vert \leq \omega$. It is easy to check that any such operator admits bounded imaginary powers, with $\Vert A^{it} \Vert \leq e^{\omega\vert t \vert$ for any $t \in \mathbbR$. We show that conversely, $A$ is similar to an $\omega$-accretive operator if $\Vert A^{it} \Vert \leq e^{\omega\vert t \vert$ for any $t \in \mathbbR$


Published: 1 January 2003
First available in Project Euclid: 18 November 2014

zbMATH: 1112.47025
MathSciNet: MR1994517

Rights: Copyright © 2003, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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