On the mutually non isomorphic spaces,II

This note is a companion to the article On the mutually non isomorphic spaces published in this journal, in which P. Cembranos and J. Mendoza showed that is a collection of mutually non isomorphic Banach spaces [5]. We now complete the picture by allowing the non‐locally convex relatives to be part of their natural family and see that, in fact, no two members of the extended class are isomorphic. Our approach is novel in the sense that we reach the isomorphism obstructions from the perspective of bases techniques and the different convexities of the spaces, both methods being intrinsic to quasi‐Banach spaces.