Unitary stable ranks and norm-one ranks

2016/04/05 by Mortini, Raymond
#13J99 #Commutative Algebra (math.AC) #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46J10 #Secondary 46J20

paper · doi:10.48550/arxiv.1604.01176

Abstract

In the context of commutative C^*-algebras we solve a problem related to a question of M. Rieffel by showing that the all-units rank and the norm-one rank coincide with the topological stable rank. We also introduce the notion of unitary M-stable rank for an arbitrary commutative unital ring and compare it with the Bass stable rank. In case of uniform algebras, a sufficient condition for norm-one reducibility is given.

Related

• Ranks of operators in simple C*-algebras with stable rank one
• Axiomatizability of the stable rank of C*-algebras
• Bounded rank of C*-algebras
• Tracial approximate divisibility and stable rank one
• The Stable Rank of C*-modules