The nLab page on Banach spaces (<http://ncatlab.org/nlab/show/Banach%20space>) was recently criticised as being, in effect, too heavily biased to category theory (*not* of the Baire kind) and not enough reflecting how Banach spaces are treated "in the real world" (or the closest approximation thereof that functional analysts live in). A couple of functional analysts have stepped in and are helping out, but I thought I'd also ask here just to see if there was anything more that we were missing.

So far, we have the following notions of morphism and isomorphism:

1. Morphisms are continuous (aka bounded) linear maps, isomorphisms are linear homeomorphisms (aka bi-Lipschitz linear equivalences).
2. Morphisms are "short maps", aka continuous linear maps of norm at most 1, isomorphisms are isometries.

Are there any others that are in reasonably common use or do we have them all?