Characterization of compact operators between certain BK spaces
نویسنده
چکیده
We give a survey of the known results concerning the sets c0(Λ), c(Λ) and c∞(Λ) including their basic topological properties, their first and second dual spaces, and the characterizations of matrix transformations from them into the spaces l∞, c and c0. Furthermore, we establish some new results such as the representations of the general bounded linear operators from c(Λ) into the spaces l∞, c and c0, and estimates for their Hausdorff measures of noncompactness. Finally, we apply our results to characterize some classes of compact operators on c0(Λ), c(Λ) and c∞(Λ). We also generalize a classical result by Cohen and Dunford which states that a regular matrix operator cannot be compact.
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