2017
Том 69
№ 6

All Issues

On simple $n$-tuples of subspaces of a Hilbert space

Samoilenko Yu. S., Strilets O. V.

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Abstract

This survey is devoted to the structure of “simple” systems $S = (H;H_1,…,H_n)$ of subspaces $H_i,\; i = 1,…, n,$ of a Hilbert space $H$, i.e., $n$-tuples of subspaces such that, for each pair of subspaces $H_i$ and $H_j$, the angle $0 < θ_{ij} ≤ π/2$ between them is fixed. We give a description of “simple” systems of subspaces in the case where the labeled graphs naturally associated with these systems are trees or unicyclic graphs and also in the case where all subspaces are one-dimensional. If the cyclic range of a graph is greater than or equal to two, then the problem of description of all systems of this type up to unitary equivalence is *-wild.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 12, pp 1956-1994.

Citation Example: Samoilenko Yu. S., Strilets O. V. On simple $n$-tuples of subspaces of a Hilbert space // Ukr. Mat. Zh. - 2009. - 61, № 12. - pp. 1668-1703.

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