Metric characterizations II

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).