Uniformly PoMBased Cuntz semigroups and approximate intertwinings
Abstract
We study topological aspects of the category of abstract Cuntz semigroups, termed Cu. We provide a suitable setting in which we are able to uniformly control how to approach an element of a Cusemigroup by a rapidly increasing sequence. This approximation induces a semimetric on the set of Cumorphisms, generalizing Cumetrics that had been constructed in the past for some particular cases. Further, we develop an approximate intertwining theory for the category Cu. Finally, we give several applications such as the classification of unitary elements of any unital AFalgebra by means of the functor Cu.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.08901
 Bibcode:
 2021arXiv210708901C
 Keywords:

 Mathematics  Operator Algebras
 EPrint:
 29 pages  (Revision after submission to International Journal of Mathematics: dfn of uniform basis has been adjusted for a better fit, e.g, the Cuntz sg of the CAR algebra has a uniform basis and proof that Lsc(X,S) admits a uniform basis, where dimX =1, has been corrected)