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Singly generatedC *-algebras

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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\(n \geqslant \sqrt {k - 1} \).

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  1. Yu. A. Mitropol’skii, G. P. Khoma, and P. V. Tsynaiko, “Periodic boundary-value problem for the inhomogeneous equation of string oscillation”,Ukr. Mat. Zh.,49, No. 4, 558–565 (1997).

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Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 8, pp. 1136–1141, August, 1999.

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Rabanovich, V.I. Singly generatedC *-algebras. Ukr Math J 51, 1282–1290 (1999).

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