Metric characterizations II

TL;DR

This paper provides linear-metric characterizations of key objects in operator space theory, extending previous work, and offers new metric-based characterizations of operator algebras.

Contribution

It introduces purely linear-metric characterizations for unitaries, operator spaces, systems, and algebras, advancing the understanding of their structure through metric properties.

Findings

Characterizations of unitaries and unital operator spaces using matrix norms

Metric descriptions of operator systems and algebras

New insights into operator algebra structures

Abstract

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).