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\(n \geqslant \sqrt {k - 1} \).
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References
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).
Additional information
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). https://doi.org/10.1007/BF02592518
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DOI: https://doi.org/10.1007/BF02592518