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Semi-simplicity of a proper weak H * -algebra

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  • Parfeny P. Saworotnow

Abstract

A weak right H * -algebra is a Banach algebra A which is a Hilbert space and which has a dense subset D r with the property that for each x in D r there exists x r such that ( y x , z ) = ( y , z x r ) for all y , z in A . It is shown that a proper (each x r is unique) weak right H * -algebra is semi-simple. Also there is an example of weak right H * -algebra which is not a left H * -algebra.

Suggested Citation

  • Parfeny P. Saworotnow, 1992. "Semi-simplicity of a proper weak H * -algebra," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 15, pages 1-3, January.
    • Handle: RePEc:hin:jijmms:807518
    DOI: 10.1155/S0161171292000541
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