On norm closed ideals in L(l p ,l q ) Academic Article uri icon

abstract

  • It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for X = ℓp (1 ≤ p < ∞) or X = c o is the ideal of compact operators. The next natural question is to describe all closed ideals of L(ℓp ⊕ ℓq) for 1 ≤ p, q < ∞, p ≠ q, or equivalently, the closed ideals in L(ℓp, ℓq) for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in L(ℓp, ℓq), including one that has not been studied before. The proofs use various methods from Banach space theory. © Instytut Matematyczny PAN, 2007.

author list (cited authors)

  • Sari, B., Schlumprecht, T. h., Tomczak-Jaegermann, N., & Troitsky, V. G.

citation count

  • 20

publication date

  • January 2007