2006/12/05 by Huaxin Lin, Lin, Huaxin · 5 citations
Mathematics · #46L05 #46L80 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.math/0612125
openalex publication_date 2006/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a finite CW complex and let h1, h2: C(X)→ A be two unital \hm s, where A is a unital C*-algebra. We study the problem when h1 and h2 are approximately homotopic. We present a K-theoretical necessary and sufficient condition for them to be approximately homotopic under the assumption that A is a unital separable simple C*-algebra of tracial rank zero, or A is a unital purely infinite simple C*-algebra. When they are approximately homotopic, we also give a bound for the length of the homotopy. Suppose that h: C(X)→ A is a monomorphism and u∈ A is a unitary (with [u]=\0\ in K1(A)). We prove that, for any \ep>0, and any compact subset \cal F⊂ C(X), there exists \dt>0 and a finite subset \cal G⊂ C(X) satisfying the following: if ‖[h(f), u]‖