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Mathematics > Functional Analysis
Title: On $\mathfrak{L}_{\infty}$-liftings of the Gelfand-Naimark morphism
(Submitted on 3 Mar 2024)
Abstract: Let $M$ be a $W^{\ast}$-algebra acting on a separable complex Hilbert space $H$. We show that the inclusion of $M$ into $\mathscr{B}(H)$ factors through an $\mathfrak{L}_{\infty}$-space only if $M$ is a finite type $\mathrm{I}$ algebra.
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