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On quadruples of projectors connected by a linear relation

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Abstract

We describe the set of γ ∈ ℝ for which there exist quadruples of projectors P i for a fixed collection of numbers αi   ℝ+, \(i = \overline {1,4} \), such that α1 P 1 + α2 P 2 + α3 P 3 + α3 P 4 = γI.

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References

  1. M. V. Zavodovs’kyi and Yu. S. Samoilenko, “Theory of operators and involutive representations of algebras,” Ukr. Mat. Visn., 1, No. 4, 532–547 (2004).

    MathSciNet  Google Scholar 

  2. S. A. Kruglyak and A. V. Roiter, “Locally scalar representations of graphs in the category of Hilbert spaces,” Funkts. Anal. Prilozhen., 39, No. 2, 13–30 (2005).

    MathSciNet  Google Scholar 

  3. M. A. Vlasenko, A. S. Mellit, and Yu. S. Samoilenko, “On algebras generated by linearly connected generators with given spectrum,” Funkts. Anal. Prilozhen., 39, No. 3, 14–27 (2005).

    MathSciNet  Google Scholar 

  4. S. A. Kruglyak, S. V. Popovich, and Yu. S. Samoilenko, “*-Representation of algebras associated with Dynkin graphs and Horn’s problem,” Uchen. Zap. Tavrich. Univ., Ser. Mat. Mekh. Inform. Kiber., 16(55), No. 2, 132–139 (2003).

    Google Scholar 

  5. A. A. Kirichenko, “On linear combinations of orthoprojectors,” Uchen. Zap. Tavrich. Univ., Ser. Mat. Mekh. Inform. Kiber., No. 2, 31–39 (2002).

  6. S. A. Kruglyak, V. I. Rabanovich, and Yu. S. Samoilenko, “On sums of projectors,” Funkts. Anal. Prilozhen., 36, No. 3, 20–35 (2002).

    MathSciNet  Google Scholar 

  7. V. S. Shulman, “On representations of limit relations,” Meth. Funct. Anal. Top., No. 4, 85–86 (2001).

    Google Scholar 

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

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1289–1295, September, 2006.

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Yusenko, K.A. On quadruples of projectors connected by a linear relation. Ukr Math J 58, 1462–1470 (2006). https://doi.org/10.1007/s11253-006-0146-x

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  • DOI: https://doi.org/10.1007/s11253-006-0146-x

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