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The spectral type of sums of operators on non-Hilbertian Banach lattices

Journal of the Australian Mathematical Society , Volume 84, Issue 02, April 2008, pp 193-198

Ian Doust and Gilles Lancien

Address: School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia

Email:  i.doust@unsw.edu.au

Abstract: It is known that on a Hilbert space the sum of a well-bounded operator and a commuting real scalar-type spectral operator is well-bounded. It had been asked whether this may still hold for operators on $L^p$ spaces for $p \ne 2$. We show here that this conjecture is false.



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