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VOL. 44 | 2010 Local Quadratic Estimates and the Holomorphic Functional Calculi
Andrew J. Morris

Editor(s) Andrew Hassell, Alan McIntosh, Robert Taggart


We construct holomorphic functional calculi and introduce local quadratic estimates for operators in a reflexive Banach space that are bisectorial except possibly in a neighbourhood of the origin. The main result is an equivalence of local quadratic estimates with bounded holomorphic functional calculi. For operators with spectrum in a neighbourhood of the origin, the results are weaker than those for bisectorial operators. For operators with a spectral gap in a neighbourhood of the origin, the results are stronger. In each case, however, local quadratic estimates are a more appropriate tool than standard quadratic estimates for establishing that our functional calculi are bounded. This shows that in certain applications it suffices to establish local quadratic estimates.


Published: 1 January 2010
First available in Project Euclid: 18 November 2014

zbMATH: 1226.47016
MathSciNet: MR2655382

Rights: Copyright © 2010, 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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