Abstract
If $A,B$ are sectorial operators on a Hilbert space with the same domain and range, and if $\parallel Ax \parallel \approx \parallel Bx \parallel$ and $\parallel A^{-1}x\parallel \approx \parallel B^{-1}x \approx$, then it is a result of Auscher, McIntosh and Nahmod that if $A$ has an $H^\infty$-calculus then so does $B$. On an arbitrary Banach space this is true with the additional hypothesis on B that it is almost R-sectorial as was shown by the author, Kunstmann and Weis in a recent preprint. We give an alternative approach to this result.
Information
Published: 1 January 2007
First available in Project Euclid: 18 November 2014
zbMATH: 1160.47013
MathSciNet: MR2328513
Rights: Copyright © 2007, 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.
