Complete continuity properties for the Fremlin projective tensor product of Orlicz sequence spaces and Banach lattices (Q618661)

The paper under review continues the study of preservation of the complete continuity property and the analytic complete continuity property when forming tensor products of Banach lattices. It culminates in the following result: \(\ell_\varphi\hat{\otimes}_F X\) has the [analytic] complete continuity property if and only if the Orlicz sequence space \(\ell_\varphi\) and the Banach lattice \(X\) both have the [analytic] complete continuity property; here, \(\hat{\otimes}_F\) denotes the Fremlin projective tensor product. This extends \textit{P. N. Dowling}'s result [Bull. Aust. Math. Soc. 73, No. 1, 37--45 (2006; Zbl 1114.46053)] that \(\ell_p\hat{\otimes}_F X, 1<p<\infty\), has the [analytic] complete continuity property exactly when \(X\) has the [analytic] complete continuity property.