Abstract:
Model representations are constructed for a system {Bk}n1 of bounded linear selfadjoint operators in
a Hilbert space H such that
[Bk,Bs]=i2φ∗R−k,sφ,σkφBs−σsφBk=R+k,sφ,σkφφ∗σs−σsφφ∗σk=2iR−k,s,1⩽k,s⩽n,
where φ is a linear operator from H into a Hilbert space E and
{σk,R±k,s}n1 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 {Bk}n1 is described.
Bibliography: 11 titles.
Keywords:
systems of selfadjoint operators, commutation relations, model representations.
Citation:
V. A. Zolotarev, “Model representations for systems of selfadjoint operators satisfying commutation relations”, Sb. Math., 201:10 (2010), 1461–1493