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Principal groupoid $C^*$-algebras with bounded trace

2007
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Proceedings of the American Mathematical Society
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Suppose G is a second countable, locally compact, Hausdorff, principal groupoid with a fixed left Haar system. We define a notion of integrability for groupoids and show G is integrable if and only if the groupoid C * -algebra C * (G) has bounded trace. Let A be a C * -algebra. An element a of the positive cone A + of A is called a bounded-trace element if the map π → tr(π(a)) is bounded on the spectrum of A; the linear span of the bounded-trace elements is a two-sided * -ideal in A. We say A

doi:10.1090/s0002-9939-07-09035-1
fatcat:clbnwuayrrei7b7ecttjgjxqsi