Similarity of operators on $l^{p}$

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 $B(l^{p})$.