Completeness of the system of root vectors of 2 × 2 upper triangular infinite-dimensional hamiltonian operators in symplectic spaces and applications

Abstract

The authors investigate the completeness of the system of eigen or root vectors of the 2 × 2 upper triangular infinite-dimensional Hamiltonian operator H ₀. First, the geometrical multiplicity and the algebraic index of the eigenvalue of H ₀ are considered. Next, some necessary and sufficient conditions for the completeness of the system of eigen or root vectors of H ₀ are obtained. Finally, the obtained results are tested in several examples.

Keywords

2 × 2 upper triangular infinite-dimensional Hamiltonian operator / Eigenvector / Root vector / Completeness

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