Abstract
Increasing sequences of contractive projections on a reflexive $L^p$ space share an unconditionality property similar to that exhibited sequences of self-adjoint projections on a Hilbert space. A slight variation of this property is shown to be precisely the correct condition on a reflexive Banach space to ensure that every operator with a contractive $AC$-functional calculus is scalar-type spectral.
Information
Published: 1 January 1988
First available in Project Euclid: 18 November 2014
zbMATH: 0687.46009
MathSciNet: MR1009593
Rights: Copyright © 1988, 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.
