Singly generatedC *-algebras

  • V. I. Rabanovych

Abstract

We consider a $C*$-algebra $A$ generated by $k$ self-adjoint elements. We prove that, for $n \geqslant \sqrt {k - 1}$ , the algebra $M_n (A)$ is singly generated, i.e., generated by one non-self-adjoint element. We present an example of algebraA for which the property that $M_n (A)$ is singly generated implies the relation $n \geqslant \sqrt {k - 1}$.
Published
25.08.1999
How to Cite
RabanovychV. I. “Singly GeneratedC *-Algebras”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 8, Aug. 1999, pp. 1136-41, https://umj.imath.kiev.ua/index.php/umj/article/view/4707.
Section
Short communications