Generalized Unitaries and the Picard Group
نویسنده
چکیده
After discussing some basic facts about generalized module maps, we use the representation theory of the algebra Ba(E) of adjointable operators on a Hilbert B–module E to show that the quotient of the group of generalized unitaries on E and its normal subgroup of unitaries on E is a subgroup of the group of automorphisms of the range ideal BE of E in B. We determine the kernel of the canonical mapping into the Picard group of BE in terms of the group of quasi inner automorphisms of BE . As a by-product we identify the group of bistrict automorphisms of the algebra of adjointable operators on E modulo inner automorphisms as a subgroup of the (opposite of the) Picard group. This work is supported by research fonds of the University of Molise.
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