Model representations for systems of selfadjoint operators satisfying commutation relations
- V.N. Karazin Kharkov National University, Kharkov (Ukraine)
Model representations are constructed for a system {l_brace}B{sub k}{r_brace}{sub 1}{sup n} of bounded linear selfadjoint operators in a Hilbert space H such that; [B{sub k},B{sub s}] = i/2 {phi}*R{sub k,s}{sup -}{phi}, {sigma}{sub k}{phi}B{sub s} - {sigma}{sub s}{phi}B{sub k}=R{sub k,s}{sup +}{phi}, {sigma}{sub k}{phi}{phi}*{sigma}{sub s}-{sigma}{sub s}{phi}{phi}*{sigma}{sub k}=2iR{sub k,s}{sup -}, 1{<=}k, s{<=}n; where {phi} is a linear operator from H into a Hilbert space E and {l_brace}{sigma}{sub k},R{sub k,s}{sup {+-}}{r_brace}{sub 1}{sup n} are some selfadjoint operators in E. A realization of these models in function spaces on a Riemann surface is found and a full set of invariants for {l_brace}B{sub k}{r_brace}{sub 1}{sup n} is described. Bibliography: 11 titles.
- OSTI ID:
- 21570923
- Journal Information:
- Sbornik. Mathematics, Vol. 201, Issue 10; Other Information: DOI: 10.1070/SM2010v201n10ABEH004118; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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