  We prove that for compatible weakly nonlocal Hamiltonian and symplectic
operators, hierarchies of infinitely many commuting local symmetries and
conservation laws can be generated under some easily verified conditions no
matter whether the generating Nijenhuis operators are weakly nonlocal or not.
We construct a recursion operator of the two dimensional periodic Volterra
chain from its Lax representation and prove that it is a Nijenhuis operator.
Furthermore we show this system is a (generalised) bi-Hamiltonian system.
Rather surprisingly, the product of its weakly nonlocal Hamiltonian and
symplectic operators gives rise to the square of the recursion operator.
