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The paper is devoted to systems of subspaces H1, . . . , Hn of a complex Hilbert space H that satisfy the following conditions: for every index i > 1, the angle θ1,i ∈ (0, π/2) between H1 and Hi is fixed; the projections onto H2k and H2k+1 commute for 1 ≤ k ≤ m (m is a fixed nonnegative number satisfying m ≤ (n−1)/2); all other pairs Hi, Hj are orthogonal. The main tool in the study is a construction of a system of subspaces in a Hilbert space on the basis of its Gram operator (the G-construction).

Systems of subspaces in Hilbert space that obey certain conditions, on their pairwise angles