Skip to main content
Log in

Quintuplets of orthoprojectors associated by a linear relation

  • Published:
Ukrainian Mathematical Journal Aims and scope

We consider the equation α1 P 1 + α2 P 2 + … α n P n = I over orthoprojectors P 1, … ,P n in a Hilbert space. We show that the set of real parameters (α1, … α n ) for which there exists a solution of this equation in orthoprojectors contains an open set from ℝ5.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. Ostrovskyi and Yu. Samoilenko, “Introduction to the theory of representation of finitely presented *-algebras. 1. Representation by bounded operators,” Rev. Math. Math. Phys., 11, 1–261 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  2. 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 

  3. S. A. Kruglyak, “Coxeter functor for a certain class of *-quivers and *-algebras,” Meth. Funct. Anal. Top., 8, No. 4, 49–57 (2002).

    MATH  MathSciNet  Google Scholar 

  4. A. A. Kyrychenko and S. A. Kruhlyak, “On the spectrum of a sum of projectors,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauky, No. 1, 24–31 (2003).

  5. K. A. Yusenko, “On quadruples of projectors associated by a linear relation,” Ukr. Mat. Zh., 58, No. 9, 1289–1295 (2006).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 5, pp. 701–710, May, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yusenko, A.A. Quintuplets of orthoprojectors associated by a linear relation. Ukr Math J 61, 834–846 (2009). https://doi.org/10.1007/s11253-009-0240-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-009-0240-y

Keywords

Navigation