Operators on Asymptotic ℓ_p Spaces which are not Compact Perturbations of a Multiple of the Identity

2009/08/08 by Beanland, Kevin
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0908.1107

Abstract

We give sufficient conditions on an asymptotic ℓ_p (for 1 < p < ∞) Banach space which ensure the space admits an operator which is not a compact perturbation of a multiple of the identity. These conditions imply the existence of strictly singular non-compact operators on the HI spaces constructed by G. Androulakis and the author and by I. Deliyanni and A. Manoussakis. Additionally we show that under these same conditions on the space X, ℓ_∞ embeds isomorphically into the space of bounded linear operators on X.

Related

• Strictly singular operators in asymptotic ℓ_p Banach spaces
• Strictly singular non-compact diagonal operators on HI spaces
• Strictly singular non-compact operators between L_p spaces
• A characterization of compact operators on ℓ^p-spaces
• The complete separation of the two finer asymptotic ℓ_p structures for 1≤ p<∞