  The present paper is a sequel to our paper "Metric characterization of
isometries and of unital operator spaces and systems". We characterize certain
common objects in the theory of operator spaces (unitaries, unital operator
spaces, operator systems, operator algebras, and so on), in terms which are
purely linear-metric, by which we mean that they only use the vector space
structure of the space and its matrix norms. In the last part we give some
characterizations of operator algebras (which are not linear-metric in our
strict sense described in the paper).
