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VOL. 42 | 2007 Spectral theory for linear operators on $L^1$ or $C(K)$ spaces
Ian Doust, Florence Lancien, Gilles Lancien

Editor(s) Alan McIntosh, Pierre Portal


It is known that on a Hilbert space, the sum of a real scalar-type operator and a commuting well-bounded operator is well-bounded. The corresponding property has been shown to be fail on $L^p$ spaces, for $1 \lt p \neq 2 \lt \infty$. We show that it does hold however on every Banach space X such that $X$ or $X*% is a Grothendieck space. This class notably includes $L^1$ and $C(K)$ spaces.


Published: 1 January 2007
First available in Project Euclid: 18 November 2014

zbMATH: 1170.47021
MathSciNet: MR2328509

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.


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