Singly generatedC ^*-algebras

Abstract

We consider aC ^*-algebraA generated byk self-adjoint elements. We prove that, for\(n \geqslant \sqrt {k - 1} \), the algebraM _n (A) is singly generated, i.e., generated by one non-self-adjoint element. We present an example of algebraA for which the property thatM _n (A) is singly generated implies the relation\(n \geqslant \sqrt {k - 1} \).