The algebra of bounded linear operators\break on ℓ p ⊕ ℓ p has infinitely many closed ideals Academic Article uri icon


  • We prove that in the reflexive range 1 < p < q < ∞, the algebra Ⅎ(ℓp⊕ℓq) of all bounded linear operators on ℓp ⊕ ℓq has infinitely many closed ideals. This solves a problem raised by A. Pietsch [4, Problem 5.3.3] in his book 'Operator ideals'.

author list (cited authors)

  • Schlumprecht, T., & Zsák, A.

citation count

  • 10

publication date

  • June 2015