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Operator equalities related to the quantumE(2) group

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Abstract

The paper deals with normal operatorsR andS satisfying simple commutation relations that we encounter investigating the quantum deformation of theE(2) group. We show thatR+S admits a normal extension if and only ifR −1 S satisfies a certain spectral condition. A number of related formulae are derived. In particular, all the functionsf satisfying the character equationf(R+S)=f(R)f(S) are found.

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References

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  3. Woronowicz, S.L.: QuantumE(2) group and its Pontryagin dual (will appear in Lett. Math. Phys.)

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Authors and Affiliations

  1. Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoża 74, PL-00-682, Warszawa, Poland

    S. L. Woronowicz

  2. Institute of Mathematics, U.R.A. CNRS no 746, Claude Bernard University, Lyon I, France

    S. L. Woronowicz

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  1. S. L. Woronowicz
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Communicated by K. Gawedzki

Supported in equal parts by the grant of the Ministry of Education of Poland and by CNRS France

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Woronowicz, S.L. Operator equalities related to the quantumE(2) group. Commun.Math. Phys. 144, 417–428 (1992). https://doi.org/10.1007/BF02101100

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  • DOI: https://doi.org/10.1007/BF02101100

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