CMA Research Report

MRR03-007

Closed ideals in the Banach algebra of operators on a Banach space

Abstract:  In general, little is known about the lattice of closed ideals in the Banach algebra B(E) of all bounded, linear operators on a Banach space E. We list the (few) Banach spaces for which this lattice is completely understood, and we give a survey of partial results for a number of other Banach spaces. We then investigate the lattice of closed ideals in B(E) where E is one of Figiel's reflexive Banach spaces not isomorphic to their Cartesian squares. Our main result is that this lattice is uncountable.

AMS Classification:  47L10, 46H10, 47L20, 46B03
Date:  23 September 2003

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