Abstract
It is known that there is a continuous linear functional on L ∞ which is not narrow. On the other hand, every order-to-norm continuous AM-compact operator from L ∞(μ) to a Banach space is narrow. We study order-to-norm continuous operators acting from L ∞(μ) with a finite atomless measure μ to a Banach space. One of our main results asserts that every order-to-norm continuous operator from L ∞(μ) to c 0(Γ) is narrow while not every such an operator is AM-compact.
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Krasikova, I., Martín, M., Merí, J. et al. On order structure and operators in L ∞(μ). centr.eur.j.math. 7, 683–693 (2009). https://doi.org/10.2478/s11533-009-0047-y
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DOI: https://doi.org/10.2478/s11533-009-0047-y