On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles - Popova, N.D.; Samoilenko, Y.S. (Symmetry, Integrability and Geometry: Methods and Applications, 2006)
For a class of *-algebras, where *-algebra AΓ,τ is generated by projections associated with vertices of graph Γ and depends on a parameter τ (0 < τ ≤ 1), we study the sets ΣΓ of values of τ such that the algebras AΓ,τ have nontrivial *-representations, by using the theory of spectra of graphs. In other words, we study such values of τ that the corresponding configurations of subspaces in a Hilbert space exist.