2006
DOI: 10.1007/s11253-006-0167-5
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On spectral theorems for families of linearly connected self-adjoint operators with given spectra associated with extended Dynkin graphs

Abstract: We prove spectral theorems for families of linearly connected self-adjoint operators with given special spectra associated with extended Dynkin graphs. We establish that all irreducible families of linearly connected operators with arbitrary spectra associated with extended Dynkin graphs are finite-dimensional.

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Cited by 14 publications
(14 citation statements)
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“…" D˙1 for a p < t < b p ; .p; t; "/ ¤ where a p and b p are defined by (11). The projection of the set M to the plane .p; t/ is presented in Fig.…”
Section: Range Of Values Of Independent Parametersmentioning
confidence: 99%
“…" D˙1 for a p < t < b p ; .p; t; "/ ¤ where a p and b p are defined by (11). The projection of the set M to the plane .p; t/ is presented in Fig.…”
Section: Range Of Values Of Independent Parametersmentioning
confidence: 99%
“…We assign two N -dimensional G-vectors (N = m + n) to the representation T : the dimension d = {d(j)} j∈Qv where d(j) = dim T (j), and the character χ = {χ(j)} j∈Qv defined above (see (5), (6)). Two orthoscalar representations T and T are equivalent if there are exist unitary matrices U = diag{U i 1 , .…”
Section: On the Indecomposability In The Category Of Representations mentioning
confidence: 99%
“…For example, the papers [30,1,37,31] are devoted to the investigation of orthoscalar n-tuples of subspaces of the Hilbert space H:…”
Section: Simple N-tuples Of Subspaces In a Hilbert Spacementioning
confidence: 99%