Metric characterizations of isometries and of unital operator spaces and systems

TL;DR

This paper provides new characterizations of unitaries, isometries, and various operator space structures using only their vector space and operator space properties, simplifying their identification.

Contribution

It introduces novel characterizations of key operator algebraic objects relying solely on their vector space and operator space structures.

Findings

New vector space-based characterizations of unitaries and isometries

Simplified criteria for identifying unital operator spaces and systems

Characterizations applicable to C*-algebras and related objects

Abstract

We give some new characterizations of unitaries, isometries, unital operator spaces, unital function spaces, operator systems, C*-algebras, and related objects. These characterizations only employ the vector space and operator space structure.