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On pairs of quadratically related operators

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Abstract

The problem of describing, up to similarity, pairs of quadratically related operators on a finite-dimensional complex linear space is studied.

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References

  1. P. Donovan and M. R. Freislich, The Representation Theory of Finite Graphs and Associated Algebras, Carleton Math. Lecture Notes, vol. 5, Carleton Univ., Ottawa, 1973.

    Google Scholar 

  2. Yu. A. Drozd, in: Representations and Quadratic Forms, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev, 1979, 39–74.

    Google Scholar 

  3. S. A. Kruglyak, Dokl. Akad. Nauk SSSR, 153:6 (1963), 1253–1256.

    MathSciNet  Google Scholar 

  4. I. M. Gelfand and V. A. Ponomarev, Funkts. Anal. Prilozhen., 3:4 (1969), 81–82; English transl.: Functional Anal. Appl., 3: 4 (1969), 325–326.

    MathSciNet  Google Scholar 

  5. Yu. A. Drozd, Funkts. Anal. Prilozhen., 6:4 (1972), 41–43; English transl.: Functional Anal. Appl., 6: 4 (1972), 286–288.

    MathSciNet  Google Scholar 

  6. V. L. Ostrovskyi and Yu. S. Samoilenko, “Introduction to the theory of representations of finitely presented *-algebras, I: Representations by bounded operators,” Rev. Math. Math. Phys., 11:1 (1999).

    Google Scholar 

  7. V. L. Ostrovskii and Yu. S. Samoilenko, Zap. Nauchn. Sem. LOMI, 172 (1989), 121–129; English transl.: J. Soviet Math., 59: 5 (1992), 1107–1113.

    Google Scholar 

  8. V. L. Ostrovskyĭ and Yu. S. Samoĭilenko, Seminar Sophus Lie, 3 (1993), 185–218.

    MathSciNet  MATH  Google Scholar 

  9. M. V. Akhramovich and M. A. Muratov, Tavricheskii Vestn. Inf. Mat., 2010, No. 2, 17–25.

    Google Scholar 

  10. M. Hoshino and J. Miyachi, Tsukuba J. Math., 12:1 (1988), 65–93.

    MathSciNet  MATH  Google Scholar 

  11. Y. Han, J. Algebra, 247:1 (2002), 57–77.

    Article  MathSciNet  MATH  Google Scholar 

  12. V. Bavula and V. Bekkert, Comm. Algebra, 28:11 (2000), 5067–5100.

    Article  MathSciNet  MATH  Google Scholar 

  13. I. M. Gelfand and V. A. Ponomarev, Uspekhi Mat. Nauk, 23:2 (1968), 3–59; English transl.: Russian Math. Surveys, 23: 2 (1968), 1–58.

    MathSciNet  Google Scholar 

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Correspondence to V. L. Ostrovskyi.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 47, No. 1, pp. 82–87, 2013

Original Russian Text Copyright © by V. L. Ostrovskyi and Yu. S. Samoilenko

This work was supported in part by DFG grant no. SCHM1009/4-1 and by SFBR-RFBR joint grant no. F40.01/008.

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Ostrovskyi, V.L., Samoilenko, Y.S. On pairs of quadratically related operators. Funct Anal Its Appl 47, 67–71 (2013). https://doi.org/10.1007/s10688-013-0009-9

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  • DOI: https://doi.org/10.1007/s10688-013-0009-9

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