Induced and coinduced Banach Lie-Poisson spaces and integrability

The Poisson induction and coinduction procedures are used to construct Banach Lie-Poisson spaces as well as related systems of integrals in involution. This general method applied to the Banach Lie-Poisson space of trace class operators leads to infinite Hamiltonian systems of k-diagonal trace class operators which have infinitely many integrals. The bidiagonal case is investigated in detail. (C) 2008 Elsevier Inc. All rights reserved.