In the explicit form, we deduce formulas for all quadruples of orthoprojectors P 1 , P 2 , P 3 , and P 4 irreducible to within unitary equivalence and connected by the linear relationship α1 P 1 + α2 P 2 + α3 P 3 + α4 P 4 = λI, where (α1, α2, α3, α4) ∈ ℝ+.
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References
S. Albeverio, V. Ostrovskyi, and Yu. Samoilenko, “On functions on graphs and representations of a certain class of *-algebra,” J. Algebra, 308, 567–582 (2007).
S. A. Kruglyak, V. I. Rabanovich, and Yu. S. Samoilenko, “On the sums of orthoprojectors,” Funkts. Anal. Prilozh., 36, Issue 3, 20–35 (2002).
K. A. Yusenko, “On quadruples of projectors connected by a linear relationship,” Ukr. Mat. Zh., 58, No. 9, 1289–1295 (2006).
A. A. Kirichenko, “On linear combinations of orthoprojectors,” Uch. Zap. Tavrich. Univ., 54, No. 2, 31–39 (2002).
V. Ostrovskyi and Yu. Samoilenko, “Introduction to the theory of representations of finitely presented *-algebras. 1. Representations by bounded operators,” Rev. Math. Math. Phys., 11, Part 1 (1999).
S. A. Kruglyak, L. A. Nazarova, and A. V. Roiter, On Regular Locally Scalar Representations of the Graph 4 in Hilbert Spaces, arXiv:math. RT/06/10931.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 2, pp. 255–264, February, 2010.
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Yusenko, A.A. Quadruples of orthoprojectors connected by a linear relationship. Ukr Math J 62, 289–301 (2010). https://doi.org/10.1007/s11253-010-0351-5
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DOI: https://doi.org/10.1007/s11253-010-0351-5