This question is intended for Banach-space specialists and so I will not repeat all the definitions here. My aim is to find out how the Banach space community refers to such spaces in discussions, and how they go about looking up information on such spaces, given that it does not seem easy to get focused results when searching online.


To be a little more precise: are such spaces referred to by anyone as "approximate $L\_p$-spaces" or "local $L\_p$-spaces"? It seems less than ideal to have an important notion described only by literal typography.


By the way: I am aware of the original papers of Lindenstrauss–Pelczynski and Lindenstrauss–Rosenthal, so that is not my question. My question is about the terminology or description that specialists in Banach space theory would use to refer to these spaces, when asking each other questions or giving each other outlines of proofs.



Verbal description, or terminology, for the ${\mathcal L}_p$-spaces of Lindenstrauss and Pelczynski
Just so that this question can be marked as answered: Bill Johnson states in comments that those in the know call these Banach spaces "script $L\_p$-spaces", and I trust his awareness/judgement of the norms in the community.


I was hoping that in the years since the foundational work, other terminology might have emerged; but so it goes.


