essential codimension

We prove that a large class of Paschke dual algebras of simple unital C*-algebras are $K_1$-injective. As a consequence, we obtain interesting $KK$-uniqueness theorems which generalize the Brown--Douglas--Fillmore essential codimension property.

a project to generalize the notion of essential codimension due to Brown–Douglas–Fillmore, as well as to understand its ramifications.

We look for generalizations of the Brown--Douglas--Fillmore essential codimension result, leading to interesting local uniqueness theorems in $KK$-theory. We also study the structure of Paschke dual algebras.

Kadison characterized the diagonals of projections and observed the presence of an integer, which Arveson later recognized as a Fredholm index obstruction applicable to any normal operator with finite spectrum coincident with its essential spectrum …

Kadison's Pythagorean theorem (2002) provides a characterization of the diagonals of projections with a subtle integrality condition. Arveson (2007), Kaftal, Ng, Zhang (2009), and Argerami (2015) all provide different proofs of that integrality …