Soft operators in C*-algebras
Journal article, 2024

We say that a C⁎-algebra is soft if it has no nonzero unital quotients, and we connect this property to the Hjelmborg-Rørdam condition for stability and to property (S) of Ortega-Perera-Rørdam. We further say that an operator in a C⁎-algebra is soft if its associated hereditary subalgebra is, and we provide useful spectral characterizations of this concept. Of particular interest are C⁎-algebras that have an abundance of soft elements in the sense that every hereditary subalgebra contains an almost full soft element. We show that this property is implied by the Global Glimm Property, and that every C⁎-algebra with an abundance of soft elements is nowhere scattered. This sheds new light on the long-standing Global Glimm Problem of whether every nowhere scattered C⁎-algebra has the Global Glimm Property.

Soft operators

Cuntz semigroups

C -Algebras ⁎

Global Glimm Problem

Author

Hannes Thiel

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Eduard Vilalta Vila

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Journal of Mathematical Analysis and Applications

0022-247X (ISSN) 1096-0813 (eISSN)

Vol. 536 1 128167

Subject Categories

Mathematics

DOI

10.1016/j.jmaa.2024.128167

More information

Latest update

3/15/2024