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THE SPECTRAL TYPE OF SUMS OF OPERATORS ON NON-HILBERTIAN BANACH LATTICES
Published online by Cambridge University Press: 01 April 2008
Abstract
T. A. Gillespie showed that on a Hilbert space the sum of a well-bounded operator and a commuting real scalar-type spectral operator is well-bounded. A longstanding question asked whether this might still hold true for operators on Lp spaces for . We show here that this conjecture is false. Indeed for a large class of reflexive spaces, the above property characterizes Hilbert space.
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- Copyright © 2008 Australian Mathematical Society