Closed ideals in the Banach algebra of operators on classical non-separable spaces

The classical result of Gohberg, Markus and Feldman states that, when E is one of the classical Banach sequence spaces E = l(p) for 1 <= p < infinity or E = c(0), the only closed, two-sided, non-trivial ideal in 5(E), the Banach algebra of operators on a Banach space E, is K(E), the ideal of compact operators. Gramsch and Luft completely classified the closed, two-sided ideals in B(H) for an arbitrary Hilbert space H through the idea of kappa-compact operators, for infinite cardinals kappa. This paper presents an extension of this result to the non-separable versions of l(p) and c(0).