Generalized unitaries and the Picard group

After discussing some basic facts about generalized module maps, we use the representation theory of the algebra ℬ^a(E) of adjointable operators on a HilbertB-moduleE to show that the quotient of the group of generalized unitaries onE and its normal subgroup of unitaries onE is a subgroup of the group of automorphisms of the range idealB _E ofE inB. We determine the kernel of the canonical mapping into the Picard group ofB _E in terms of the group of quasi inner automorphisms ofB _E . As a by-product we identify the group of bistrict automorphisms of the algebra of adjointable operators onE modulo inner automorphisms as a subgroup of the (opposite of the) Picard group.