# Remarks on Essential Codimension

## TL;DR

This paper explores generalizations of the essential codimension concept in operator algebras, aiming to establish local uniqueness theorems in KK-theory and analyze Paschke dual algebras.

## Contribution

It introduces new generalizations of essential codimension and investigates the structure of Paschke dual algebras, extending classical results in operator K-theory.

## Key findings

- Derived local uniqueness theorems in KK-theory.
- Analyzed the structure of Paschke dual algebras.
- Extended the Brown-Douglas-Fillmore essential codimension results.

## Abstract

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.