been christened \[11-15\] as the augmented version of superfield formalism (AVSF). One of the key observations of the applications of USF and AVSF is the fact that the group structure of the (non-)Abelian gauge theories remains somewhat [*hidden*]{} but the geometry of these theories becomes quite explicit as we take the help of the cohomological operators of differential geometry.

The purpose of our present investigation is to exploit the theoretical strength of AVSF to derive the superspace [*dual*]{} unitary operators for the 1$D$ and 2$D$ interesting models of the Abelian 1-form gauge theories corresponding to the (anti-)dual BRST \[i.e., (anti-)co-BRST\] symmetry transformations which have been shown to exist for the above models. These models are the 1$D$ rigid rotor, modified versions of the 2$D$ Proca as well as anomalous gauge theories and 2$D$ self-dual bosonic field theory. In fact, these models have been shown to provide the physical examples of Hodge theory within the framework of BRST formalsm where the (anti-)BRST as well as (anti-)co-BRST symmetries exist together with a unique bosonic symmetry and the ghost-scale symmetry \[16-20\]. The universal superspace (SUSP) [*unitary*]{} operators, corresponding to the nilpotent (anti-)BRST symmetry transformations, have already been shown to exist for the above 