Erratum : "The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces" (Journal of Functional Analysis (2004) vol. 214 (106-131) 10.1016.j.jfa.2004.02.009)

Laustsen, Niels Jakob and Loy, Richard J. and Read, Charles J. (2005) Erratum : "The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces" (Journal of Functional Analysis (2004) vol. 214 (106-131) 10.1016.j.jfa.2004.02.009). Journal of Functional Analysis, 220 (1). pp. 240-241. ISSN 0022-1236

Abstract

Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra BðEÞ of all (bounded, linear) operators on E is fully understood. Indeed, upto now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c0 and cp for 1ppoN: We add a new member to this family by showing that there are exactly four closed ideals in BðEÞ for the Banach space E :¼ ð"cn2 Þc0 ; that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces c1 2; c2 2;y; cn2 ;y . r