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A Resolvent Approach to the Real Quantum Plane

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Abstract

Let q ≠ ± 1 be a complex number of modulus one. This paper deals with the operator relation AB = qBA for self-adjoint operators A and B on a Hilbert space. Two classes of well-behaved representations of this relation are studied in detail and characterized by resolvent equations.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Tereshchenkivska 3, Kiev, 01601, Ukraine

    Vasyl Ostrovskyi

  2. Mathematisches Institut, Universität Leipzig, Augustusplatz 9/10, 04109, Leipzig, Germany

    Konrad Schmüdgen

Authors
  1. Vasyl Ostrovskyi
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  2. Konrad Schmüdgen
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Correspondence to Konrad Schmüdgen.

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Dedicated to Professor Yurii S. Samoilenko on the occasion of his 70th birthday

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Ostrovskyi, V., Schmüdgen, K. A Resolvent Approach to the Real Quantum Plane. Integr. Equ. Oper. Theory 79, 451–476 (2014). https://doi.org/10.1007/s00020-014-2165-6

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  • DOI: https://doi.org/10.1007/s00020-014-2165-6

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