representation of a Cc(G)*- topological algebra

Definition 0.1   A representation of a $ C_c({\mathsf{G}})$ topological $ *$ -algebra is defined as a continuous $ *$ -morphism from $ C_c({\mathsf{G}})$ to $ B(\H )$ , where $ {\mathsf{G}}$ is a topological groupoid, (usually a locally compact groupoid, $ {\mathsf{G}}_{lc}$ ), $ \H$ is a Hilbert spacehttp://planetphysics.org/encyclopedia/NormInducedByInnerProduct.html, and $ B(\H )$ is the $ C^*$ -algebra of bounded linear operators on the Hilbert space $ \H$ ; of course, one considers the inductive limit (strong) topology to be defined on $ C_c({\mathsf{G}})$ , and then also an operator weak topology to be defined on $ B(\H )$ .



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