Induction for weak symplectic Banach manifolds (Q931157)

This paper extends the symplectic induction procedure to the case of weak symplectic Banach manifolds. On weak symplectic manifolds not all smooth functions admit a Hamiltonian vector field. The authors first introduce the Poisson subalgebra of smooth functions that admit Hamiltonian vector fields. The symplectic induction procedure on weak symplectic manifolds is then presented. The theory is finally applied to several examples of Banach manifolds, namely, the Banach Lie group of \(k\)-diagonal operators. Explicit formulas are also obtained.