The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces
نویسندگان
چکیده
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 `p for 1 6 p < ∞. 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 := (⊕ `2 ) c0 , that is, E is the c0-direct sum of the nite-dimensional Hilbert spaces `2, ` 2 2, . . . , ` n 2 , . . .
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