-cross products and a generalized quantum mechanical -body problem.
Circular operators related to the operator of multiplication by a homomorphism of a locally compact abelian group and its restrictions are completely characterized. As particular cases descriptions of circular operators related to various quantum observables are given.
Let and be mutually commuting unital C* subalgebras of (). It is shown that and are C* independent if and only if for all natural numbers n, m, for all n-tuples A = (A₁, ..., Aₙ) of doubly commuting nonzero operators of and m-tuples B = (B₁, ..., Bₘ) of doubly commuting nonzero operators of , , where Sp denotes the joint Taylor spectrum.