The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces

摘要

Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra M(E) of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c(0) and l(p) for 1 less than or equal to p < infinity. We add a new member to this family by showing that there are exactly four closed ideals in M(E) for the Banach space E that is, E is the c(0)-direct sum of the finite-dimensional Hilbert spaces l(2)(1), l(2)(2),...,l(2)(n)... . (C) 2004 Elsevier Inc. All rights reserved.