Commutators on (∑ℓq)ℓ1


Let T be a bounded linear operator on X=(∑ℓq)ℓ1 with 1≤. q<. ∞. T is said to be X-strictly singular if the restriction of T on any subspace of X that is isomorphic to X is not an isomorphism. It is shown that the unique proper maximal ideal in L(X) is the set of all X-strictly singular operators. With some more efforts, we prove that T is a commutator in L(X) if and only if for all non-zero λ∈C, the operator T- λ. I is not X-strictly singular. © 2013 Elsevier Inc.

Publication Title

Journal of Mathematical Analysis and Applications