On approximation properties related to unconditionally p‐compact operators and Sinha–Karn p‐compact operators

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 .