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- W3208953722 abstract "We consider the graph whose vertex set is a conjugacy class C consisting of finite-rank self-adjoint operators on a complex Hilbert space H. The dimension of H is assumed to be not less than 3. In the case when operators from C have two eigenvalues only, we obtain the Grassmann graph formed by k-dimensional subspaces of H, where k is the smallest dimension of eigenspaces. Chow's theorem describes automorphisms of this graph for k>1. Under the assumption that operators from C have more than two eigenvalues we show that every automorphism of the graph is induced by a unitary or anti-unitary operator up to a permutation of eigenspaces with the same dimensions. In contrast to this result, Chow's theorem states that there are graph automorphisms induced by semilinear automorphisms not preserving orthogonality if C is formed by operators with precisely two eigenvalues." @default.
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- W3208953722 date "2023-10-01" @default.
- W3208953722 modified "2023-09-27" @default.
- W3208953722 title "Automorphisms of graphs corresponding to conjugacy classes of finite-rank self-adjoint operators" @default.
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- W3208953722 doi "https://doi.org/10.1016/j.laa.2023.06.001" @default.
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