Abstract
AbstractWe establish new results on the ‐approximation property for the Banach operator ideal of the unconditionally p‐compact operators in the case of . As a consequence of our results, we provide a negative answer for the case of a problem posed by Kim. Namely, the ‐approximation property implies neither the ‐approximation property nor the (classical) approximation property; and the ‐approximation property implies neither the ‐approximation property nor the approximation property. Here, denotes the p‐compact operators of Sinha and Karn for . We also show for all that there is a closed subspace that fails the ‐approximation property for all .
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