# The C*-algebra of compact perturbations of diagonal operators

## TL;DR

This paper investigates the structure of a specific C*-algebra formed by diagonal operators plus compact operators, analyzing its unitary group, ideals, automorphisms, and projections.

## Contribution

It provides a detailed structural analysis of the C*-algebra of compact perturbations of diagonal operators, including its automorphisms and ideals.

## Key findings

- Describes the unitary group structure.
- Classifies the ideals within the algebra.
- Analyzes automorphisms and projections.

## Abstract

We study the elementary C*-algebra whose elements are the sum of a diagonal plus a compact operator. We describe the structure of the unitary group, the sets of ideals, automorhisms and projections.