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Structure theorems for families of idempotents

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Abstract

For *-algebras generated by idempotents and orthoprojectors, we study the complexity of the problem of description of *-representations to within unitary equivalence. In particular, we prove that the *-algebra generated by two orthogonal idempotents is *-wild as well as the *-algebra generated by three orthoprojectors, two of which are orthogonal.

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Authors and Affiliations

  1. Kiev Institute of Control and Communications, Kiev

    S. A. Kruglyak

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    Yu S. Samoilenko

Authors
  1. S. A. Kruglyak
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  2. Yu S. Samoilenko
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 4, pp. 523–533, April, 1998.

This work was partially supported by the State Foundation for Fundamental Research of the Ukrainian Ministry for Science and Technology.

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Kruglyak, S.A., Samoilenko, Y.S. Structure theorems for families of idempotents. Ukr Math J 50, 593–604 (1998). https://doi.org/10.1007/BF02487391

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  • DOI: https://doi.org/10.1007/BF02487391

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