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Journal of the London Mathematical Society 1997 56(3):595-606; doi:10.1112/S0024610797005486
© 1997 by London Mathematical Society
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© The London Mathematical Society

Quasinilpotent Operators and the Invariant Subspace Problem

C. J. Read

Trinity College Cambridge CB2 1TQ. E-mail: cr25{at}cus.cam.ac.uk

Received 22 May 1995.

In this paper we construct quasinilpotent operators without nontrivial invariant subspaces. As well as being interesting in its own right, we believe that this is a sensible (perhaps necessary) first step for addressing the difficult problem of constructing topologically simple Banach algebras.


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