Commutators on (∑ℓq)ℓ1
Abstract
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
Recommended Citation
Zheng, B. (2014). Commutators on (∑ℓq)ℓ1. Journal of Mathematical Analysis and Applications, 413 (1), 284-290. https://doi.org/10.1016/j.jmaa.2013.11.066
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