The Case Where the Sum of Three Partial Reflections is Equal to Zero
- 25 Downloads
Up to unitary equivalence, we describe all irreducible triples of self-adjoint operators A1, A2, A3 such that σ(Ai) ⊂ |−1, 0, 1}, i = 1, 2, 3, and A1 + A2 + A3 = 0.
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- 1.A. A. Klyachko, “Stable bundles, representation theory and Hermitian operators,” Selecta Math., 4, 419-445 (1998).Google Scholar
- 2.W. Fulton, “Eigenvalues, invariant factors, highest weights, and Schubert calculus,” Bull. Amer. Math. Soc., 37, No. 3, 209-249 (2000).Google Scholar
- 3.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).Google Scholar
- 4.V. I. Rabanovich and Yu. S. Samoilenko, “Scalar operators representable as a sum of projectors,” Ukr. Mat. Zh., 53, No. 7, 939-952 (2001).Google Scholar
- 5.S. A. Kruglyak, V. I. Rabanovich, and Yu. S. Samoilenko, “On sums of projectors,” Funkts. Anal. Prilozhen., 36, Issue 3, 20-35 (2002).Google Scholar
- 6.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).Google Scholar
- 7.B. Morrel and P. Muhly, “Centered operators,” Stud. Math., 51, 251-263 (1974).Google Scholar
- 8.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).Google Scholar
© Plenum Publishing Corporation 2003