# Journal of Operator Theory

Volume 37, Issue 1, Winter 1997 pp. 121-154.

Almost multiplicative morphisms and some applications**Authors**: Huaxin Lin

**Author institution:**Department of Mathematics, East China Normal University, Shanghai 200062, CHINA Current address: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222, U.S.A.

**Summary:**We show that, for any $\varepsilon > 0$ and an integer n > 0, there exists $\delta > 0$ such that if x_1, x_2,..., x_n are normal elements in the unit ball of a purely infinite simple C*-algebra A with

$\left\| {x_i x_j - x_j x_i } \right\| < \delta \quad i = 1,2,...,n$

then there exist mutually commuting normal elements y_1, y_2,..., $y_n \in A$ such that

$\left\| {x_i - y_i } \right\| < \varepsilon \quad i = 1,2,...,n$

**Keywords:**C*-algebra, C*-algebra homomorphism, almost multiplicative morphisms.

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