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LIMITS OF HOMOMORPHISMS WITH FINITE-DIMENSIONAL RANGE

SHANWEN HU

Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China

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HUAXIN LIN

Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China

Department of Mathematics, University of Oregon, Eugene 97403–1222, USA

Current:

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, and

YIFENG XUE

Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P. R. China

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https://doi.org/10.1142/S0129167X05003089Cited by:3 (Source: Crossref)

Abstract

Let X be a compact metric space and A be a unital simple C*-algebra with TR(A)=0. Suppose that ϕ : C(X) → A is a unital monomorphism. We study the problem when ϕ can be approximated by homomorphisms with finite-dimensional range. We give a K-theoretical necessary and sufficient condition for ϕ being approximated by homomorphisms with finite-dimensional range.

Keywords:

AMSC: 46L05, 46L35

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