We study the duality of r-compact operator. We establish if an operator T: E → F is r-compact, then its adjoint T′: F′ → E′ is also r-compact. We also provide some sufficient condition on the pair of Banach lattices E and F which guarantees that a regular operator T: E → F such that T′: F′ → E′ is r-compact, must itself be r-compact.
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