# Similarity of operators on $l^{p}$

## TL;DR

This paper extends operator similarity results on l^p spaces, proving a version of Voiculescu's absorption theorem, establishing group structure for certain Ext groups, and demonstrating homotopy invariance for separable Banach algebras.

## Contribution

It introduces new similarity and homotopy invariance results for operators on l^p spaces, generalizing classical operator theory to Banach algebra contexts.

## Key findings

- Proves a version of Voiculescu's absorption theorem for l^p operators.
- Shows Ext groups are groups for certain Banach algebras.
- Establishes homotopy invariance of Ext groups in specific Banach algebra settings.

## Abstract

For $1<p<\infty$, we prove (i) a version of Voiculescu's absorption theorem for operators on $l^{p}$, (ii) that $\mathrm{Ext}_{\sim,s}(\mathcal{A},K(l^{p}))$ is a group for certain Banach algebra $\mathcal{A}$, and (iii) homotopy invariance of $\mathrm{Ext}_{\sim,s}(\mathcal{A},K(l^{p}))^{-1}$ in $\mathcal{A}$ for separable Banach algebra $\mathcal{A}$ that is isomorphic to a subalgebra of $B(l^{p})$.