# Journal of Operator Theory

Volume 40, Issue 2, Fall 1998 pp. 217-275.

Almost multiplicative morphisms and almost commuting matrices**Authors**: Guihua Gong (1), and Huaxin Lin (2)

**Author institution:**(1) Department of Mathematics, University of Puerto Rico, Rio Piedras, San Juan, PR 00931, U.S.A.

(2) Department of Mathematics, University of Oregon, Eugene, Oregon 97403--1222, U.S.A.

**Summary:**We prove that a contractive positive linear map which is approximately multiplicative and approximately injective from $C(X)$ into certain unital simple $C^*$-algebras of real rank zero and stable rank one is close to a homomorphism (with finite dimensional range) if a necessary $K$-theoretical obstruction vanishes and dimension of $X$ is no more than two. We also show that the above is false it the dimension of $X$ is greater than 2, in general.

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