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Defining metric spaces via operators from unital C∗-algebras

1998
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Pacific Journal of Mathematics
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For a unital C * -algebra A and an operator T with DomT ⊆ A, RangeT in a normed space, and ker T = Cmathrm1, we consider the metric d T on S(A), the state space of A, given by d T (φ, ψ) = sup{|φ(a) − ψ(a)| : a ∈ A & T a ≤ 1}, for φ, ψ ∈ S(A). This is a generalization of the definition given by A. Connes for defining a metric on S(A) via unbounded Fredholm modules over A. The main problem of our investigation, posed by M. Rieffel, is the relationship between thus defined metric topology T dT ,

doi:10.2140/pjm.1998.186.285
fatcat:4t2qb2yfs5atrl3gyqucxddcxm