Abstract
Up to unitary equivalence, we describe all irreducible triples of self-adjoint operators A 1, A 2, A 3 such that σ(A i) ⊂ |−1, 0, 1}, i = 1, 2, 3, and A 1 + A 2 + A 3 = 0.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. A. Klyachko, “Stable bundles, representation theory and Hermitian operators,” Selecta Math., 4, 419-445 (1998).
W. Fulton, “Eigenvalues, invariant factors, highest weights, and Schubert calculus,” Bull. Amer. Math. Soc., 37, No. 3, 209-249 (2000).
V. I. Rabanovich and Yu. S. Samoilenko, “The case where the sum of idempotents or projectors is a multiple of the identity,” Funkts. Anal. Prilozhen., 34, Issue 4, 91-93 (2000).
V. I. Rabanovich and Yu. S. Samoilenko, “Scalar operators representable as a sum of projectors,” Ukr. Mat. Zh., 53, No. 7, 939-952 (2001).
S. A. Kruglyak, V. I. Rabanovich, and Yu. S. Samoilenko, “On sums of projectors,” Funkts. Anal. Prilozhen., 36, Issue 3, 20-35 (2002).
S. A. Kruglyak and A. V. Roiter, “Locally scalar representations of graphs in the category of Hilbert spaces,” in: Locally Scalar Representations and Separating Functions [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2003).
B. Morrel and P. Muhly, “Centered operators,” Stud. Math., 51, 251-263 (1974).
V. Ostrovskii and Yu. Samoilenko, “Introduction to the theory of representations of finitely presented *-algebras. 1. Representations by bounded operators,” Rev. Math. Math. Phys., 11, 1-261 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mellit, A.S. The Case Where the Sum of Three Partial Reflections is Equal to Zero. Ukrainian Mathematical Journal 55, 1542–1550 (2003). https://doi.org/10.1023/B:UKMA.0000018015.10875.e2
Issue Date:
DOI: https://doi.org/10.1023/B:UKMA.0000018015.10875.e2