Ulam stability for some classes of C*-algebras

Abstract

We prove some stability results for certain classes of C*-algebras. We prove that whenever $A$ is a finite-dimensional C*-algebra, $B$ is a C*-algebra and $\phi\colon A\to B$ is approximately a $^*$-homomorphism then there is an actual $^*$-homomorphism close to $\phi$ by a factor depending only on how far is $\phi$ from being a $^*$-homomorphism and not on $A$ or $B$.