Previous issue ·  Next issue ·  Most recent issue in the archive · All issues in the archive   

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.

Keywords:  Almost multiplicative morphisms, almost commuting matrices


Contents    Full-Text PDF