Abstract
An example is given of a linear transformation which defines a wellbounded operator on $L^p[O, 1] for 1 \leq p \leq \infty$. It is shown that the properties of the decomposition of the identity associated with this operator (and consequently the type of functional calculus that the operator admits) vary markedly depending on the domain space.
Information
Published: 1 January 1990
First available in Project Euclid: 18 November 2014
zbMATH: 0718.47018
MathSciNet: MR1060113
Rights: Copyright © 1990, 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.
