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On transitive systems of subspaces in a Hilbert space. (English) Zbl 1103.47015

Let \(H\) be a Hilbert space and \(H_{1},H_{2},\dots,H_{n}\) be \(n\) subspaces of \(H\) and let \(S=(H;H_{1},H_{2},\dots,H_{n})\) denote the system of \(n\) subspaces of the space \(H\).
In the paper under review, the authors analyze the complexity of the description problem for transitive systems of subspaces \(S=(H;H_{1},H_{2},\dots,H_{n})\) for \(n \geq 5\). Also, they prove that the problem of describing inequivalent \(*\)-representations of the \(*\)-algebras that give rise to nonisomorphic transitive systems is \(*\)-wild.

MSC:

47A62 Equations involving linear operators, with operator unknowns
16G20 Representations of quivers and partially ordered sets
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