CMA Research Report

MRR03-005

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

Abstract:  Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra B(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 c₀ and l_p for 1 < p < oo. We add a new member to this family by showing that there are exactly four closed ideals in B(E) for the Banach space E := ( (+) l₂ⁿ )_{c0}, that is, E is the c₀-direct sum of the finite-dimensional Hilbert spaces l₂¹, l₂², ..., l₂ⁿ, ...

AMS Classification:  47L10
Date:  17 June 2003

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