2012/07/30 by Hu, Shanwen, Xue, Yifeng
#46L35 #47D25 #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1207.6890
In this short note, we prove that for a C^*-algebra å generated by n elements, Mk(å) is generated by k mutually unitarily equivalent and almost mutually orthogonal projections for any k≥ \de(n)=min\k∈\mathbb N | (k-1)(k-2)≥ 2n\. Then combining this result with recent works of Nagisa, Thiel and Winter on the generators of C^*--algebras, we show that for a C^*-algebra å generated by finite number of elements, there is d≥ 3 such that Md( A) is generated by three mutually unitarily equivalent and almost mutually orthogonal projections. Furthermore, for certain separable purely infinite simple unital C^*--algebras and AF--algebras, we give some conditions that make them be generated by three mutually unitarily equivalent and almost mutually orthogonal projections.