Geodesic
Factorization in the Invertible Group of a C*-Algebra
Canadian journal of mathematics, Tome 49 (1997) no. 6, pp. 1188-1205

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In this paper we consider the following problem: Given a unital C*- algebra A and a collection of elements S in the identity component of the invertible group of A, denoted inv0(A), characterize the group of finite products of elements of S. The particular C*-algebras studied in this paper are either unital purely infinite simple or of the form (A ⊗ K)+, where A is any C*-algebra and K is the compact operators on an infinite dimensional separable Hilbert space. The types of elements used in the factorizations are unipotents (1+ nilpotent), positive invertibles and symmetries (s2 = 1). First we determine the groups of finite products for each collection of elements in (A ⊗ K)+. Then we give upper bounds on the number of factors needed in these cases. The main result, which uses results for (A ⊗ K)+, is that for A unital purely infinite and simple, inv0(A) is generated by each of these collections of elements.
DOI : 10.4153/CJM-1997-058-7
Mots-clés : 46L05 
Leen, Michael J. Factorization in the Invertible Group of a C*-Algebra. Canadian journal of mathematics, Tome 49 (1997) no. 6, pp. 1188-1205. doi: 10.4153/CJM-1997-058-7
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