An algebraic approach to the radius of comparison
An algebraic approach to the radius of comparison
The radius of comparison is an invariant for unital C$^*$-algebras which extends the theory of covering dimension to noncommutative spaces. We extend its definition to general C$^*$-algebras, and give an algebraic (as opposed to functional-theoretic) reformulation. This yields new permanence properties for the radius of comparison which strengthen its analogy …