Reduction of Exponential Rank in Direct Limits of C*-Algebras

Phillips, N. Christopher

Canadian journal of mathematics, Tome 46 (1994) no. 4, pp. 818-853

Résumé

We prove the following result. Let A be a direct limit of direct sums ofC *-algebras of the form C(X) ⊗ Mn , with the spaces X being compact metric. Suppose that there is a finite upper bound on the dimensions of the spaces involved, and suppose that A is simple. Then the C * exponential rank of A is at most 1 + ε, that is, every element of the identity component of the unitary group of A is a limit of exponentials. This is true regardless of whether the real rank of A is 0 or 1.

Détail

DOI : 10.4153/CJM-1994-047-7

Mots-clés : 46L05

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