When almost multiplicative morphisms are close to homomorphisms

Lin, Huaxin

doi:10.1090/S0002-9947-99-02310-7

When almost multiplicative morphisms are close to homomorphisms
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Trans. Amer. Math. Soc. 351 (1999), 5027-5049 Request permission

Abstract:

It is shown that approximately multiplicative contractive positive morphisms from $C(X)$ (with dim $X\le 2$) 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 homomorphism $h: C(X)\to A$ is approximated by homomorphisms with finite dimensional range, if $h$ gives no $K$-theoretical obstacle.

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