When almost multiplicative morphisms close to homomorphisms

Abstract. It is shown that approximately multiplicative contractive positive morphisms from C(X) (with dim X ≤ 2) into a simple C-algebra A of real rank zero and of stable rank one are close to homomorphisms, provided that certain K-theoretical obstacles vanish. As a corollary we show that a ho-momorphism h: C(X) → A is approximated by homomorphisms with finite dimensional range, if h gives no K-theoretical obstacle. Let X be a compact metric space and let A be a C-algebra. A contractive positive linear map : C(X) ! A is said to be -F-multiplicative if k (fg) − (f) (g)k < for all f 2 F: A homomorphism is certainly -F-multiplicative. The proble