The Hamiltonian system and completeness of symplectic orthogonal system (Q1369476)

Two new Banach spaces \(ZH_a\) and \(ZH_b\) are obtained. It is shown the completeness of the eigenfunction system (symplectic orthogonal system) of a class of Hamiltonian systems in the spaces \(ZH_a\) and \(ZH_b\). Also, it is proven that the \(ZH_b\) space can be continuously imbedded in \(V \times V\), where \(V\) is a Hilbert space. It is established that \(ZH_b \neq L_2[0,1] \times L_2 [0,1]\).