2019
Том 71
№ 10

All Issues

Singly generatedC *-algebras

Rabanovych V. I.

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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 $n \geqslant \sqrt {k - 1}$.

English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 8, pp 1282–1290.

Citation Example: Rabanovych V. I. Singly generatedC *-algebras // Ukr. Mat. Zh. - 1999. - 51, № 8. - pp. 1136-1141.

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