N=2 superintegrable f-Toda mapping and super-NLS hierarchy in (1 vertical bar 2) superspace

A new integrable N = 2 supersymmetric f-Toda mapping in (1 \ 2) superspace, acting like the symmetry transformation of N = 2 supersymmetric NLS hierar chy, is proposed. The first two Hamiltonian structures and the recursion op erator connecting all evolution systems and Hamiltonian structures of the N = 2 super-NLS hierarchy are constructed explicitly by using only the condi tions of invariance with respect to the f-Toda mapping. A new representatio n for its Hamiltonians is observed.