Similarity of operators on $l^p$

For $1<p<\mathrm{\infty }$, we prove (i) a version of Voiculescu’s absorption theorem for operators on $l^p$, (ii) that ${\mathrm{E}\mathrm{x}\mathrm{t}}_{\sim ,s}(\mathcal{A},K(l^p))$ is a group for certain Banach algebra $\mathcal{A}$, and (iii) homotopy invariance of ${\mathrm{E}\mathrm{x}\mathrm{t}}_{\sim ,s}(\mathcal{A},K(l^p){)}^{-1}$ in $\mathcal{A}$ for separable Banach algebra $\mathcal{A}$ that is isomorphic to a subalgebra of $B(l^p)$.