TY - JOUR
T1 - The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces
AU - Laustsen, Niels Jakob
AU - Loy, Richard J.
AU - Read, Charles J.
PY - 2004/9/1
Y1 - 2004/9/1
N2 - Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra ℬ (B) 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 ℓp for 1≤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:=(⊕ℓ2n) c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ℓ2 1,ℓ22,...,ℓ2 n,...
AB - Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra ℬ (B) 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 ℓp for 1≤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:=(⊕ℓ2n) c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ℓ2 1,ℓ22,...,ℓ2 n,...
KW - Banach algebra
KW - Banach space
KW - Ideal lattice
KW - Operator
UR - http://www.scopus.com/inward/record.url?scp=4043124784&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2004.02.009
DO - 10.1016/j.jfa.2004.02.009
M3 - Article
SN - 0022-1236
VL - 214
SP - 106
EP - 131
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -